Identifier
Identifier
Values
[] generating graphics... => 1
[1] generating graphics... => 2
[2] generating graphics... => 3
[1,1] generating graphics... => 3
[3] generating graphics... => 4
[2,1] generating graphics... => 6
[1,1,1] generating graphics... => 4
[4] generating graphics... => 5
[3,1] generating graphics... => 9
[2,2] generating graphics... => 6
[2,1,1] generating graphics... => 9
[1,1,1,1] generating graphics... => 5
[5] generating graphics... => 6
[4,1] generating graphics... => 12
[3,2] generating graphics... => 12
[3,1,1] generating graphics... => 14
[2,2,1] generating graphics... => 12
[2,1,1,1] generating graphics... => 12
[1,1,1,1,1] generating graphics... => 6
[6] generating graphics... => 7
[5,1] generating graphics... => 15
[4,2] generating graphics... => 18
[4,1,1] generating graphics... => 19
[3,3] generating graphics... => 10
[3,2,1] generating graphics... => 26
[3,1,1,1] generating graphics... => 19
[2,2,2] generating graphics... => 10
[2,2,1,1] generating graphics... => 18
[2,1,1,1,1] generating graphics... => 15
[1,1,1,1,1,1] generating graphics... => 7
[7] generating graphics... => 8
[6,1] generating graphics... => 18
[5,2] generating graphics... => 24
[5,1,1] generating graphics... => 24
[4,3] generating graphics... => 20
[4,2,1] generating graphics... => 40
[4,1,1,1] generating graphics... => 26
[3,3,1] generating graphics... => 24
[3,2,2] generating graphics... => 24
[3,2,1,1] generating graphics... => 40
[3,1,1,1,1] generating graphics... => 24
[2,2,2,1] generating graphics... => 20
[2,2,1,1,1] generating graphics... => 24
[2,1,1,1,1,1] generating graphics... => 18
[1,1,1,1,1,1,1] generating graphics... => 8
[8] generating graphics... => 9
[7,1] generating graphics... => 21
[6,2] generating graphics... => 30
[6,1,1] generating graphics... => 29
[5,3] generating graphics... => 30
[5,2,1] generating graphics... => 54
[5,1,1,1] generating graphics... => 33
[4,4] generating graphics... => 15
[4,3,1] generating graphics... => 51
[4,2,2] generating graphics... => 39
[4,2,1,1] generating graphics... => 62
[4,1,1,1,1] generating graphics... => 33
[3,3,2] generating graphics... => 30
[3,3,1,1] generating graphics... => 39
[3,2,2,1] generating graphics... => 51
[3,2,1,1,1] generating graphics... => 54
[3,1,1,1,1,1] generating graphics... => 29
[2,2,2,2] generating graphics... => 15
[2,2,2,1,1] generating graphics... => 30
[2,2,1,1,1,1] generating graphics... => 30
[2,1,1,1,1,1,1] generating graphics... => 21
[1,1,1,1,1,1,1,1] generating graphics... => 9
[9] generating graphics... => 10
[8,1] generating graphics... => 24
[7,2] generating graphics... => 36
[7,1,1] generating graphics... => 34
[6,3] generating graphics... => 40
[6,2,1] generating graphics... => 68
[6,1,1,1] generating graphics... => 40
[5,4] generating graphics... => 30
[5,3,1] generating graphics... => 78
[5,2,2] generating graphics... => 54
[5,2,1,1] generating graphics... => 84
[5,1,1,1,1] generating graphics... => 42
[4,4,1] generating graphics... => 40
[4,3,2] generating graphics... => 68
[4,3,1,1] generating graphics... => 84
[4,2,2,1] generating graphics... => 84
[4,2,1,1,1] generating graphics... => 84
[4,1,1,1,1,1] generating graphics... => 40
[3,3,3] generating graphics... => 20
[3,3,2,1] generating graphics... => 68
[3,3,1,1,1] generating graphics... => 54
[3,2,2,2] generating graphics... => 40
[3,2,2,1,1] generating graphics... => 78
[3,2,1,1,1,1] generating graphics... => 68
[3,1,1,1,1,1,1] generating graphics... => 34
[2,2,2,2,1] generating graphics... => 30
[2,2,2,1,1,1] generating graphics... => 40
[2,2,1,1,1,1,1] generating graphics... => 36
[2,1,1,1,1,1,1,1] generating graphics... => 24
[1,1,1,1,1,1,1,1,1] generating graphics... => 10
[10] generating graphics... => 11
[9,1] generating graphics... => 27
[8,2] generating graphics... => 42
[8,1,1] generating graphics... => 39
[7,3] generating graphics... => 50
[7,2,1] generating graphics... => 82
[7,1,1,1] generating graphics... => 47
[6,4] generating graphics... => 45
[6,3,1] generating graphics... => 105
[6,2,2] generating graphics... => 69
[6,2,1,1] generating graphics... => 106
[6,1,1,1,1] generating graphics... => 51
[5,5] generating graphics... => 21
[5,4,1] generating graphics... => 84
[5,3,2] generating graphics... => 108
[5,3,1,1] generating graphics... => 129
[5,2,2,1] generating graphics... => 117
[5,2,1,1,1] generating graphics... => 114
[5,1,1,1,1,1] generating graphics... => 51
[4,4,2] generating graphics... => 60
[4,4,1,1] generating graphics... => 68
[4,3,3] generating graphics... => 50
[4,3,2,1] generating graphics... => 158
[4,3,1,1,1] generating graphics... => 117
[4,2,2,2] generating graphics... => 68
[4,2,2,1,1] generating graphics... => 129
[4,2,1,1,1,1] generating graphics... => 106
[4,1,1,1,1,1,1] generating graphics... => 47
[3,3,3,1] generating graphics... => 50
[3,3,2,2] generating graphics... => 60
[3,3,2,1,1] generating graphics... => 108
[3,3,1,1,1,1] generating graphics... => 69
[3,2,2,2,1] generating graphics... => 84
[3,2,2,1,1,1] generating graphics... => 105
[3,2,1,1,1,1,1] generating graphics... => 82
[3,1,1,1,1,1,1,1] generating graphics... => 39
[2,2,2,2,2] generating graphics... => 21
[2,2,2,2,1,1] generating graphics... => 45
[2,2,2,1,1,1,1] generating graphics... => 50
[2,2,1,1,1,1,1,1] generating graphics... => 42
[2,1,1,1,1,1,1,1,1] generating graphics... => 27
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 11
[11] generating graphics... => 12
[10,1] generating graphics... => 30
[9,2] generating graphics... => 48
[9,1,1] generating graphics... => 44
[8,3] generating graphics... => 60
[8,2,1] generating graphics... => 96
[8,1,1,1] generating graphics... => 54
[7,4] generating graphics... => 60
[7,3,1] generating graphics... => 132
[7,2,2] generating graphics... => 84
[7,2,1,1] generating graphics... => 128
[7,1,1,1,1] generating graphics... => 60
[6,5] generating graphics... => 42
[6,4,1] generating graphics... => 128
[6,3,2] generating graphics... => 148
[6,3,1,1] generating graphics... => 174
[6,2,2,1] generating graphics... => 150
[6,2,1,1,1] generating graphics... => 144
[6,1,1,1,1,1] generating graphics... => 62
[5,5,1] generating graphics... => 60
[5,4,2] generating graphics... => 132
[5,4,1,1] generating graphics... => 144
[5,3,3] generating graphics... => 84
[5,3,2,1] generating graphics... => 252
[5,3,1,1,1] generating graphics... => 180
[5,2,2,2] generating graphics... => 96
[5,2,2,1,1] generating graphics... => 180
[5,2,1,1,1,1] generating graphics... => 144
[5,1,1,1,1,1,1] generating graphics... => 60
[4,4,3] generating graphics... => 60
[4,4,2,1] generating graphics... => 144
[4,4,1,1,1] generating graphics... => 96
[4,3,3,1] generating graphics... => 132
[4,3,2,2] generating graphics... => 144
[4,3,2,1,1] generating graphics... => 252
[4,3,1,1,1,1] generating graphics... => 150
[4,2,2,2,1] generating graphics... => 144
[4,2,2,1,1,1] generating graphics... => 174
[4,2,1,1,1,1,1] generating graphics... => 128
[4,1,1,1,1,1,1,1] generating graphics... => 54
[3,3,3,2] generating graphics... => 60
[3,3,3,1,1] generating graphics... => 84
[3,3,2,2,1] generating graphics... => 132
[3,3,2,1,1,1] generating graphics... => 148
[3,3,1,1,1,1,1] generating graphics... => 84
[3,2,2,2,2] generating graphics... => 60
[3,2,2,2,1,1] generating graphics... => 128
[3,2,2,1,1,1,1] generating graphics... => 132
[3,2,1,1,1,1,1,1] generating graphics... => 96
[3,1,1,1,1,1,1,1,1] generating graphics... => 44
[2,2,2,2,2,1] generating graphics... => 42
[2,2,2,2,1,1,1] generating graphics... => 60
[2,2,2,1,1,1,1,1] generating graphics... => 60
[2,2,1,1,1,1,1,1,1] generating graphics... => 48
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 30
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 12
[12] generating graphics... => 13
[11,1] generating graphics... => 33
[10,2] generating graphics... => 54
[10,1,1] generating graphics... => 49
[9,3] generating graphics... => 70
[9,2,1] generating graphics... => 110
[9,1,1,1] generating graphics... => 61
[8,4] generating graphics... => 75
[8,3,1] generating graphics... => 159
[8,2,2] generating graphics... => 99
[8,2,1,1] generating graphics... => 150
[8,1,1,1,1] generating graphics... => 69
[7,5] generating graphics... => 63
[7,4,1] generating graphics... => 172
[7,3,2] generating graphics... => 188
[7,3,1,1] generating graphics... => 219
[7,2,2,1] generating graphics... => 183
[7,2,1,1,1] generating graphics... => 174
[7,1,1,1,1,1] generating graphics... => 73
[6,6] generating graphics... => 28
[6,5,1] generating graphics... => 125
[6,4,2] generating graphics... => 207
[6,4,1,1] generating graphics... => 220
[6,3,3] generating graphics... => 119
[6,3,2,1] generating graphics... => 346
[6,3,1,1,1] generating graphics... => 243
[6,2,2,2] generating graphics... => 124
[6,2,2,1,1] generating graphics... => 231
[6,2,1,1,1,1] generating graphics... => 182
[6,1,1,1,1,1,1] generating graphics... => 73
[5,5,2] generating graphics... => 100
[5,5,1,1] generating graphics... => 105
[5,4,3] generating graphics... => 140
[5,4,2,1] generating graphics... => 321
[5,4,1,1,1] generating graphics... => 204
[5,3,3,1] generating graphics... => 225
[5,3,2,2] generating graphics... => 234
[5,3,2,1,1] generating graphics... => 402
[5,3,1,1,1,1] generating graphics... => 231
[5,2,2,2,1] generating graphics... => 204
[5,2,2,1,1,1] generating graphics... => 243
[5,2,1,1,1,1,1] generating graphics... => 174
[5,1,1,1,1,1,1,1] generating graphics... => 69
[4,4,4] generating graphics... => 35
[4,4,3,1] generating graphics... => 165
[4,4,2,2] generating graphics... => 140
[4,4,2,1,1] generating graphics... => 234
[4,4,1,1,1,1] generating graphics... => 124
[4,3,3,2] generating graphics... => 165
[4,3,3,1,1] generating graphics... => 225
[4,3,2,2,1] generating graphics... => 321
[4,3,2,1,1,1] generating graphics... => 346
[4,3,1,1,1,1,1] generating graphics... => 183
[4,2,2,2,2] generating graphics... => 105
[4,2,2,2,1,1] generating graphics... => 220
[4,2,2,1,1,1,1] generating graphics... => 219
[4,2,1,1,1,1,1,1] generating graphics... => 150
[4,1,1,1,1,1,1,1,1] generating graphics... => 61
[3,3,3,3] generating graphics... => 35
[3,3,3,2,1] generating graphics... => 140
[3,3,3,1,1,1] generating graphics... => 119
[3,3,2,2,2] generating graphics... => 100
[3,3,2,2,1,1] generating graphics... => 207
[3,3,2,1,1,1,1] generating graphics... => 188
[3,3,1,1,1,1,1,1] generating graphics... => 99
[3,2,2,2,2,1] generating graphics... => 125
[3,2,2,2,1,1,1] generating graphics... => 172
[3,2,2,1,1,1,1,1] generating graphics... => 159
[3,2,1,1,1,1,1,1,1] generating graphics... => 110
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 49
[2,2,2,2,2,2] generating graphics... => 28
[2,2,2,2,2,1,1] generating graphics... => 63
[2,2,2,2,1,1,1,1] generating graphics... => 75
[2,2,2,1,1,1,1,1,1] generating graphics... => 70
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 54
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 33
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 13
[13] generating graphics... => 14
[12,1] generating graphics... => 36
[11,2] generating graphics... => 60
[11,1,1] generating graphics... => 54
[10,3] generating graphics... => 80
[10,2,1] generating graphics... => 124
[10,1,1,1] generating graphics... => 68
[9,4] generating graphics... => 90
[9,3,1] generating graphics... => 186
[9,2,2] generating graphics... => 114
[9,2,1,1] generating graphics... => 172
[9,1,1,1,1] generating graphics... => 78
[8,5] generating graphics... => 84
[8,4,1] generating graphics... => 216
[8,3,2] generating graphics... => 228
[8,3,1,1] generating graphics... => 264
[8,2,2,1] generating graphics... => 216
[8,2,1,1,1] generating graphics... => 204
[8,1,1,1,1,1] generating graphics... => 84
[7,6] generating graphics... => 56
[7,5,1] generating graphics... => 190
[7,4,2] generating graphics... => 282
[7,4,1,1] generating graphics... => 296
[7,3,3] generating graphics... => 154
[7,3,2,1] generating graphics... => 440
[7,3,1,1,1] generating graphics... => 306
[7,2,2,2] generating graphics... => 152
[7,2,2,1,1] generating graphics... => 282
[7,2,1,1,1,1] generating graphics... => 220
[7,1,1,1,1,1,1] generating graphics... => 86
[6,6,1] generating graphics... => 84
[6,5,2] generating graphics... => 216
[6,5,1,1] generating graphics... => 220
[6,4,3] generating graphics... => 228
[6,4,2,1] generating graphics... => 504
[6,4,1,1,1] generating graphics... => 312
[6,3,3,1] generating graphics... => 320
[6,3,2,2] generating graphics... => 324
[6,3,2,1,1] generating graphics... => 552
[6,3,1,1,1,1] generating graphics... => 312
[6,2,2,2,1] generating graphics... => 264
[6,2,2,1,1,1] generating graphics... => 312
[6,2,1,1,1,1,1] generating graphics... => 220
[6,1,1,1,1,1,1,1] generating graphics... => 84
[5,5,3] generating graphics... => 120
[5,5,2,1] generating graphics... => 248
[5,5,1,1,1] generating graphics... => 150
[5,4,4] generating graphics... => 90
[5,4,3,1] generating graphics... => 394
[5,4,2,2] generating graphics... => 318
[5,4,2,1,1] generating graphics... => 522
[5,4,1,1,1,1] generating graphics... => 264
[5,3,3,2] generating graphics... => 288
[5,3,3,1,1] generating graphics... => 384
[5,3,2,2,1] generating graphics... => 522
[5,3,2,1,1,1] generating graphics... => 552
[5,3,1,1,1,1,1] generating graphics... => 282
[5,2,2,2,2] generating graphics... => 150
[5,2,2,2,1,1] generating graphics... => 312
[5,2,2,1,1,1,1] generating graphics... => 306
[5,2,1,1,1,1,1,1] generating graphics... => 204
[5,1,1,1,1,1,1,1,1] generating graphics... => 78
[4,4,4,1] generating graphics... => 100
[4,4,3,2] generating graphics... => 220
[4,4,3,1,1] generating graphics... => 288
[4,4,2,2,1] generating graphics... => 318
[4,4,2,1,1,1] generating graphics... => 324
[4,4,1,1,1,1,1] generating graphics... => 152
[4,3,3,3] generating graphics... => 100
[4,3,3,2,1] generating graphics... => 394
[4,3,3,1,1,1] generating graphics... => 320
[4,3,2,2,2] generating graphics... => 248
[4,3,2,2,1,1] generating graphics... => 504
[4,3,2,1,1,1,1] generating graphics... => 440
[4,3,1,1,1,1,1,1] generating graphics... => 216
[4,2,2,2,2,1] generating graphics... => 220
[4,2,2,2,1,1,1] generating graphics... => 296
[4,2,2,1,1,1,1,1] generating graphics... => 264
[4,2,1,1,1,1,1,1,1] generating graphics... => 172
[4,1,1,1,1,1,1,1,1,1] generating graphics... => 68
[3,3,3,3,1] generating graphics... => 90
[3,3,3,2,2] generating graphics... => 120
[3,3,3,2,1,1] generating graphics... => 228
[3,3,3,1,1,1,1] generating graphics... => 154
[3,3,2,2,2,1] generating graphics... => 216
[3,3,2,2,1,1,1] generating graphics... => 282
[3,3,2,1,1,1,1,1] generating graphics... => 228
[3,3,1,1,1,1,1,1,1] generating graphics... => 114
[3,2,2,2,2,2] generating graphics... => 84
[3,2,2,2,2,1,1] generating graphics... => 190
[3,2,2,2,1,1,1,1] generating graphics... => 216
[3,2,2,1,1,1,1,1,1] generating graphics... => 186
[3,2,1,1,1,1,1,1,1,1] generating graphics... => 124
[3,1,1,1,1,1,1,1,1,1,1] generating graphics... => 54
[2,2,2,2,2,2,1] generating graphics... => 56
[2,2,2,2,2,1,1,1] generating graphics... => 84
[2,2,2,2,1,1,1,1,1] generating graphics... => 90
[2,2,2,1,1,1,1,1,1,1] generating graphics... => 80
[2,2,1,1,1,1,1,1,1,1,1] generating graphics... => 60
[2,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 36
[1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 14
[14] generating graphics... => 15
[13,1] generating graphics... => 39
[12,2] generating graphics... => 66
[12,1,1] generating graphics... => 59
[11,3] generating graphics... => 90
[11,2,1] generating graphics... => 138
[11,1,1,1] generating graphics... => 75
[10,4] generating graphics... => 105
[10,3,1] generating graphics... => 213
[10,2,2] generating graphics... => 129
[10,2,1,1] generating graphics... => 194
[10,1,1,1,1] generating graphics... => 87
[9,5] generating graphics... => 105
[9,4,1] generating graphics... => 260
[9,3,2] generating graphics... => 268
[9,3,1,1] generating graphics... => 309
[9,2,2,1] generating graphics... => 249
[9,2,1,1,1] generating graphics... => 234
[9,1,1,1,1,1] generating graphics... => 95
[8,6] generating graphics... => 84
[8,5,1] generating graphics... => 255
[8,4,2] generating graphics... => 357
[8,4,1,1] generating graphics... => 372
[8,3,3] generating graphics... => 189
[8,3,2,1] generating graphics... => 534
[8,3,1,1,1] generating graphics... => 369
[8,2,2,2] generating graphics... => 180
[8,2,2,1,1] generating graphics... => 333
[8,2,1,1,1,1] generating graphics... => 258
[8,1,1,1,1,1,1] generating graphics... => 99
[7,7] generating graphics... => 36
[7,6,1] generating graphics... => 174
[7,5,2] generating graphics... => 336
[7,5,1,1] generating graphics... => 335
[7,4,3] generating graphics... => 318
[7,4,2,1] generating graphics... => 687
[7,4,1,1,1] generating graphics... => 420
[7,3,3,1] generating graphics... => 415
[7,3,2,2] generating graphics... => 414
[7,3,2,1,1] generating graphics... => 702
[7,3,1,1,1,1] generating graphics... => 393
[7,2,2,2,1] generating graphics... => 324
[7,2,2,1,1,1] generating graphics... => 381
[7,2,1,1,1,1,1] generating graphics... => 266
[7,1,1,1,1,1,1,1] generating graphics... => 99
[6,6,2] generating graphics... => 150
[6,6,1,1] generating graphics... => 150
[6,5,3] generating graphics... => 270
[6,5,2,1] generating graphics... => 540
[6,5,1,1,1] generating graphics... => 315
[6,4,4] generating graphics... => 155
[6,4,3,1] generating graphics... => 645
[6,4,2,2] generating graphics... => 505
[6,4,2,1,1] generating graphics... => 819
[6,4,1,1,1,1] generating graphics... => 404
[6,3,3,2] generating graphics... => 414
[6,3,3,1,1] generating graphics... => 546
[6,3,2,2,1] generating graphics... => 723
[6,3,2,1,1,1] generating graphics... => 758
[6,3,1,1,1,1,1] generating graphics... => 381
[6,2,2,2,2] generating graphics... => 195
[6,2,2,2,1,1] generating graphics... => 404
[6,2,2,1,1,1,1] generating graphics... => 393
[6,2,1,1,1,1,1,1] generating graphics... => 258
[6,1,1,1,1,1,1,1,1] generating graphics... => 95
[5,5,4] generating graphics... => 105
[5,5,3,1] generating graphics... => 345
[5,5,2,2] generating graphics... => 255
[5,5,2,1,1] generating graphics... => 408
[5,5,1,1,1,1] generating graphics... => 195
[5,4,4,1] generating graphics... => 270
[5,4,3,2] generating graphics... => 540
[5,4,3,1,1] generating graphics... => 690
[5,4,2,2,1] generating graphics... => 726
[5,4,2,1,1,1] generating graphics... => 723
[5,4,1,1,1,1,1] generating graphics... => 324
[5,3,3,3] generating graphics... => 180
[5,3,3,2,1] generating graphics... => 690
[5,3,3,1,1,1] generating graphics... => 546
[5,3,2,2,2] generating graphics... => 408
[5,3,2,2,1,1] generating graphics... => 819
[5,3,2,1,1,1,1] generating graphics... => 702
[5,3,1,1,1,1,1,1] generating graphics... => 333
[5,2,2,2,2,1] generating graphics... => 315
[5,2,2,2,1,1,1] generating graphics... => 420
[5,2,2,1,1,1,1,1] generating graphics... => 369
[5,2,1,1,1,1,1,1,1] generating graphics... => 234
[5,1,1,1,1,1,1,1,1,1] generating graphics... => 87
[4,4,4,2] generating graphics... => 150
[4,4,4,1,1] generating graphics... => 180
[4,4,3,3] generating graphics... => 150
[4,4,3,2,1] generating graphics... => 540
[4,4,3,1,1,1] generating graphics... => 414
[4,4,2,2,2] generating graphics... => 255
[4,4,2,2,1,1] generating graphics... => 505
[4,4,2,1,1,1,1] generating graphics... => 414
[4,4,1,1,1,1,1,1] generating graphics... => 180
[4,3,3,3,1] generating graphics... => 270
[4,3,3,2,2] generating graphics... => 345
[4,3,3,2,1,1] generating graphics... => 645
[4,3,3,1,1,1,1] generating graphics... => 415
[4,3,2,2,2,1] generating graphics... => 540
[4,3,2,2,1,1,1] generating graphics... => 687
[4,3,2,1,1,1,1,1] generating graphics... => 534
[4,3,1,1,1,1,1,1,1] generating graphics... => 249
[4,2,2,2,2,2] generating graphics... => 150
[4,2,2,2,2,1,1] generating graphics... => 335
[4,2,2,2,1,1,1,1] generating graphics... => 372
[4,2,2,1,1,1,1,1,1] generating graphics... => 309
[4,2,1,1,1,1,1,1,1,1] generating graphics... => 194
[4,1,1,1,1,1,1,1,1,1,1] generating graphics... => 75
[3,3,3,3,2] generating graphics... => 105
[3,3,3,3,1,1] generating graphics... => 155
[3,3,3,2,2,1] generating graphics... => 270
[3,3,3,2,1,1,1] generating graphics... => 318
[3,3,3,1,1,1,1,1] generating graphics... => 189
[3,3,2,2,2,2] generating graphics... => 150
[3,3,2,2,2,1,1] generating graphics... => 336
[3,3,2,2,1,1,1,1] generating graphics... => 357
[3,3,2,1,1,1,1,1,1] generating graphics... => 268
[3,3,1,1,1,1,1,1,1,1] generating graphics... => 129
[3,2,2,2,2,2,1] generating graphics... => 174
[3,2,2,2,2,1,1,1] generating graphics... => 255
[3,2,2,2,1,1,1,1,1] generating graphics... => 260
[3,2,2,1,1,1,1,1,1,1] generating graphics... => 213
[3,2,1,1,1,1,1,1,1,1,1] generating graphics... => 138
[3,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 59
[2,2,2,2,2,2,2] generating graphics... => 36
[2,2,2,2,2,2,1,1] generating graphics... => 84
[2,2,2,2,2,1,1,1,1] generating graphics... => 105
[2,2,2,2,1,1,1,1,1,1] generating graphics... => 105
[2,2,2,1,1,1,1,1,1,1,1] generating graphics... => 90
[2,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 66
[2,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 39
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 15
[15] generating graphics... => 16
[14,1] generating graphics... => 42
[13,2] generating graphics... => 72
[13,1,1] generating graphics... => 64
[12,3] generating graphics... => 100
[12,2,1] generating graphics... => 152
[12,1,1,1] generating graphics... => 82
[11,4] generating graphics... => 120
[11,3,1] generating graphics... => 240
[11,2,2] generating graphics... => 144
[11,2,1,1] generating graphics... => 216
[11,1,1,1,1] generating graphics... => 96
[10,5] generating graphics... => 126
[10,4,1] generating graphics... => 304
[10,3,2] generating graphics... => 308
[10,3,1,1] generating graphics... => 354
[10,2,2,1] generating graphics... => 282
[10,2,1,1,1] generating graphics... => 264
[10,1,1,1,1,1] generating graphics... => 106
[9,6] generating graphics... => 112
[9,5,1] generating graphics... => 320
[9,4,2] generating graphics... => 432
[9,4,1,1] generating graphics... => 448
[9,3,3] generating graphics... => 224
[9,3,2,1] generating graphics... => 628
[9,3,1,1,1] generating graphics... => 432
[9,2,2,2] generating graphics... => 208
[9,2,2,1,1] generating graphics... => 384
[9,2,1,1,1,1] generating graphics... => 296
[9,1,1,1,1,1,1] generating graphics... => 112
[8,7] generating graphics... => 72
[8,6,1] generating graphics... => 264
[8,5,2] generating graphics... => 456
[8,5,1,1] generating graphics... => 450
[8,4,3] generating graphics... => 408
[8,4,2,1] generating graphics... => 870
[8,4,1,1,1] generating graphics... => 528
[8,3,3,1] generating graphics... => 510
[8,3,2,2] generating graphics... => 504
[8,3,2,1,1] generating graphics... => 852
[8,3,1,1,1,1] generating graphics... => 474
[8,2,2,2,1] generating graphics... => 384
[8,2,2,1,1,1] generating graphics... => 450
[8,2,1,1,1,1,1] generating graphics... => 312
[8,1,1,1,1,1,1,1] generating graphics... => 114
[7,7,1] generating graphics... => 112
[7,6,2] generating graphics... => 320
[7,6,1,1] generating graphics... => 312
[7,5,3] generating graphics... => 432
[7,5,2,1] generating graphics... => 840
[7,5,1,1,1] generating graphics... => 480
[7,4,4] generating graphics... => 224
[7,4,3,1] generating graphics... => 900
[7,4,2,2] generating graphics... => 692
[7,4,2,1,1] generating graphics... => 1116
[7,4,1,1,1,1] generating graphics... => 544
[7,3,3,2] generating graphics... => 540
[7,3,3,1,1] generating graphics... => 708
[7,3,2,2,1] generating graphics... => 924
[7,3,2,1,1,1] generating graphics... => 964
[7,3,1,1,1,1,1] generating graphics... => 480
[7,2,2,2,2] generating graphics... => 240
[7,2,2,2,1,1] generating graphics... => 496
[7,2,2,1,1,1,1] generating graphics... => 480
[7,2,1,1,1,1,1,1] generating graphics... => 312
[7,1,1,1,1,1,1,1,1] generating graphics... => 112
[6,6,3] generating graphics... => 200
[6,6,2,1] generating graphics... => 380
[6,6,1,1,1] generating graphics... => 216
[6,5,4] generating graphics... => 250
[6,5,3,1] generating graphics... => 786
[6,5,2,2] generating graphics... => 562
[6,5,2,1,1] generating graphics... => 888
[6,5,1,1,1,1] generating graphics... => 410
[6,4,4,1] generating graphics... => 472
[6,4,3,2] generating graphics... => 896
[6,4,3,1,1] generating graphics... => 1128
[6,4,2,2,1] generating graphics... => 1152
[6,4,2,1,1,1] generating graphics... => 1134
[6,4,1,1,1,1,1] generating graphics... => 496
[6,3,3,3] generating graphics... => 264
[6,3,3,2,1] generating graphics... => 992
[6,3,3,1,1,1] generating graphics... => 776
[6,3,2,2,2] generating graphics... => 568
[6,3,2,2,1,1] generating graphics... => 1134
[6,3,2,1,1,1,1] generating graphics... => 964
[6,3,1,1,1,1,1,1] generating graphics... => 450
[6,2,2,2,2,1] generating graphics... => 410
[6,2,2,2,1,1,1] generating graphics... => 544
[6,2,2,1,1,1,1,1] generating graphics... => 474
[6,2,1,1,1,1,1,1,1] generating graphics... => 296
[6,1,1,1,1,1,1,1,1,1] generating graphics... => 106
[5,5,5] generating graphics... => 56
[5,5,4,1] generating graphics... => 324
[5,5,3,2] generating graphics... => 492
[5,5,3,1,1] generating graphics... => 612
[5,5,2,2,1] generating graphics... => 588
[5,5,2,1,1,1] generating graphics... => 568
[5,5,1,1,1,1,1] generating graphics... => 240
[5,4,4,2] generating graphics... => 420
[5,4,4,1,1] generating graphics... => 492
[5,4,3,3] generating graphics... => 380
[5,4,3,2,1] generating graphics... => 1332
[5,4,3,1,1,1] generating graphics... => 992
[5,4,2,2,2] generating graphics... => 588
[5,4,2,2,1,1] generating graphics... => 1152
[5,4,2,1,1,1,1] generating graphics... => 924
[5,4,1,1,1,1,1,1] generating graphics... => 384
[5,3,3,3,1] generating graphics... => 492
[5,3,3,2,2] generating graphics... => 612
[5,3,3,2,1,1] generating graphics... => 1128
[5,3,3,1,1,1,1] generating graphics... => 708
[5,3,2,2,2,1] generating graphics... => 888
[5,3,2,2,1,1,1] generating graphics... => 1116
[5,3,2,1,1,1,1,1] generating graphics... => 852
[5,3,1,1,1,1,1,1,1] generating graphics... => 384
[5,2,2,2,2,2] generating graphics... => 216
[5,2,2,2,2,1,1] generating graphics... => 480
[5,2,2,2,1,1,1,1] generating graphics... => 528
[5,2,2,1,1,1,1,1,1] generating graphics... => 432
[5,2,1,1,1,1,1,1,1,1] generating graphics... => 264
[5,1,1,1,1,1,1,1,1,1,1] generating graphics... => 96
[4,4,4,3] generating graphics... => 140
[4,4,4,2,1] generating graphics... => 380
[4,4,4,1,1,1] generating graphics... => 264
[4,4,3,3,1] generating graphics... => 420
[4,4,3,2,2] generating graphics... => 492
[4,4,3,2,1,1] generating graphics... => 896
[4,4,3,1,1,1,1] generating graphics... => 540
[4,4,2,2,2,1] generating graphics... => 562
[4,4,2,2,1,1,1] generating graphics... => 692
[4,4,2,1,1,1,1,1] generating graphics... => 504
[4,4,1,1,1,1,1,1,1] generating graphics... => 208
[4,3,3,3,2] generating graphics... => 324
[4,3,3,3,1,1] generating graphics... => 472
[4,3,3,2,2,1] generating graphics... => 786
[4,3,3,2,1,1,1] generating graphics... => 900
[4,3,3,1,1,1,1,1] generating graphics... => 510
[4,3,2,2,2,2] generating graphics... => 380
[4,3,2,2,2,1,1] generating graphics... => 840
[4,3,2,2,1,1,1,1] generating graphics... => 870
[4,3,2,1,1,1,1,1,1] generating graphics... => 628
[4,3,1,1,1,1,1,1,1,1] generating graphics... => 282
[4,2,2,2,2,2,1] generating graphics... => 312
[4,2,2,2,2,1,1,1] generating graphics... => 450
[4,2,2,2,1,1,1,1,1] generating graphics... => 448
[4,2,2,1,1,1,1,1,1,1] generating graphics... => 354
[4,2,1,1,1,1,1,1,1,1,1] generating graphics... => 216
[4,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 82
[3,3,3,3,3] generating graphics... => 56
[3,3,3,3,2,1] generating graphics... => 250
[3,3,3,3,1,1,1] generating graphics... => 224
[3,3,3,2,2,2] generating graphics... => 200
[3,3,3,2,2,1,1] generating graphics... => 432
[3,3,3,2,1,1,1,1] generating graphics... => 408
[3,3,3,1,1,1,1,1,1] generating graphics... => 224
[3,3,2,2,2,2,1] generating graphics... => 320
[3,3,2,2,2,1,1,1] generating graphics... => 456
[3,3,2,2,1,1,1,1,1] generating graphics... => 432
[3,3,2,1,1,1,1,1,1,1] generating graphics... => 308
[3,3,1,1,1,1,1,1,1,1,1] generating graphics... => 144
[3,2,2,2,2,2,2] generating graphics... => 112
[3,2,2,2,2,2,1,1] generating graphics... => 264
[3,2,2,2,2,1,1,1,1] generating graphics... => 320
[3,2,2,2,1,1,1,1,1,1] generating graphics... => 304
[3,2,2,1,1,1,1,1,1,1,1] generating graphics... => 240
[3,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 152
[3,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 64
[2,2,2,2,2,2,2,1] generating graphics... => 72
[2,2,2,2,2,2,1,1,1] generating graphics... => 112
[2,2,2,2,2,1,1,1,1,1] generating graphics... => 126
[2,2,2,2,1,1,1,1,1,1,1] generating graphics... => 120
[2,2,2,1,1,1,1,1,1,1,1,1] generating graphics... => 100
[2,2,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 72
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 42
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 16
click to show generating function       
Description
The total number of Littlewood-Richardson tableaux of given shape.
This is the multiplicity of the Schur function $s_\lambda$ in $\sum_{\mu, \nu} s_\mu s_\nu$, where the sum is over all partitions $\mu$ and $\nu$.
Code
import sage.libs.lrcalc.lrcalc as lrcalc
def statistic(la):
    n = la.size()
    return sum(lrcalc.lrcoef_unsafe(la, mu, nu) for m in range(n+1) for mu in Partitions(m) for nu in Partitions(n-m))

# alternative implementation
@cached_function
def product(n):
    s = SymmetricFunctions(QQ).s()
    return sum(s(mu)*s(nu) for m in range(n+1) for mu in Partitions(m) for nu in Partitions(n-m))

def statistic(la):
    return product(la.size()).coefficient(la)

Created
May 29, 2019 at 08:07 by Martin Rubey
Updated
May 29, 2019 at 11:38 by Martin Rubey