*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St001943
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The sum of the squares of the hook lengths of an integer partition.
For a cell in the Ferrers diagram of a partition, the hook length is given by the number of boxes to its right plus the number of boxes below + 1.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(la):
return sum(h^2 for h in la.hooks())
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 5
[1,1] => 5
[3] => 14
[2,1] => 11
[1,1,1] => 14
[4] => 30
[3,1] => 22
[2,2] => 18
[2,1,1] => 22
[1,1,1,1] => 30
[5] => 55
[4,1] => 40
[3,2] => 31
[3,1,1] => 35
[2,2,1] => 31
[2,1,1,1] => 40
[1,1,1,1,1] => 55
[6] => 91
[5,1] => 67
[4,2] => 51
[4,1,1] => 55
[3,3] => 43
[3,2,1] => 46
[3,1,1,1] => 55
[2,2,2] => 43
[2,2,1,1] => 51
[2,1,1,1,1] => 67
[1,1,1,1,1,1] => 91
[7] => 140
[6,1] => 105
[5,2] => 80
[5,1,1] => 84
[4,3] => 65
[4,2,1] => 68
[4,1,1,1] => 77
[3,3,1] => 60
[3,2,2] => 60
[3,2,1,1] => 68
[3,1,1,1,1] => 84
[2,2,2,1] => 65
[2,2,1,1,1] => 80
[2,1,1,1,1,1] => 105
[1,1,1,1,1,1,1] => 140
[8] => 204
[7,1] => 156
[6,2] => 120
[6,1,1] => 124
[5,3] => 96
[5,2,1] => 99
[5,1,1,1] => 108
[4,4] => 84
[4,3,1] => 84
[4,2,2] => 84
[4,2,1,1] => 92
[4,1,1,1,1] => 108
[3,3,2] => 76
[3,3,1,1] => 84
[3,2,2,1] => 84
[3,2,1,1,1] => 99
[3,1,1,1,1,1] => 124
[2,2,2,2] => 84
[2,2,2,1,1] => 96
[2,2,1,1,1,1] => 120
[2,1,1,1,1,1,1] => 156
[1,1,1,1,1,1,1,1] => 204
[9] => 285
[8,1] => 222
[7,2] => 173
[7,1,1] => 177
[6,3] => 138
[6,2,1] => 141
[6,1,1,1] => 150
[5,4] => 117
[5,3,1] => 117
[5,2,2] => 117
[5,2,1,1] => 125
[5,1,1,1,1] => 141
[4,4,1] => 105
[4,3,2] => 102
[4,3,1,1] => 110
[4,2,2,1] => 110
[4,2,1,1,1] => 125
[4,1,1,1,1,1] => 150
[3,3,3] => 93
[3,3,2,1] => 102
[3,3,1,1,1] => 117
[3,2,2,2] => 105
[3,2,2,1,1] => 117
[3,2,1,1,1,1] => 141
[3,1,1,1,1,1,1] => 177
[2,2,2,2,1] => 117
[2,2,2,1,1,1] => 138
[2,2,1,1,1,1,1] => 173
[2,1,1,1,1,1,1,1] => 222
[1,1,1,1,1,1,1,1,1] => 285
[10] => 385
[9,1] => 305
[8,2] => 241
[8,1,1] => 245
[7,3] => 193
[7,2,1] => 196
[7,1,1,1] => 205
[6,4] => 161
[6,3,1] => 161
[6,2,2] => 161
[6,2,1,1] => 169
[6,1,1,1,1] => 185
[5,5] => 145
[5,4,1] => 140
[5,3,2] => 137
[5,3,1,1] => 145
[5,2,2,1] => 145
[5,2,1,1,1] => 160
[5,1,1,1,1,1] => 185
[4,4,2] => 125
[4,4,1,1] => 133
[4,3,3] => 121
[4,3,2,1] => 130
[4,3,1,1,1] => 145
[4,2,2,2] => 133
[4,2,2,1,1] => 145
[4,2,1,1,1,1] => 169
[4,1,1,1,1,1,1] => 205
[3,3,3,1] => 121
[3,3,2,2] => 125
[3,3,2,1,1] => 137
[3,3,1,1,1,1] => 161
[3,2,2,2,1] => 140
[3,2,2,1,1,1] => 161
[3,2,1,1,1,1,1] => 196
[3,1,1,1,1,1,1,1] => 245
[2,2,2,2,2] => 145
[2,2,2,2,1,1] => 161
[2,2,2,1,1,1,1] => 193
[2,2,1,1,1,1,1,1] => 241
[2,1,1,1,1,1,1,1,1] => 305
[1,1,1,1,1,1,1,1,1,1] => 385
[11] => 506
[10,1] => 407
[9,2] => 326
[9,1,1] => 330
[8,3] => 263
[8,2,1] => 266
[8,1,1,1] => 275
[7,4] => 218
[7,3,1] => 218
[7,2,2] => 218
[7,2,1,1] => 226
[7,1,1,1,1] => 242
[6,5] => 191
[6,4,1] => 186
[6,3,2] => 183
[6,3,1,1] => 191
[6,2,2,1] => 191
[6,2,1,1,1] => 206
[6,1,1,1,1,1] => 231
[5,5,1] => 170
[5,4,2] => 162
[5,4,1,1] => 170
[5,3,3] => 158
[5,3,2,1] => 167
[5,3,1,1,1] => 182
[5,2,2,2] => 170
[5,2,2,1,1] => 182
[5,2,1,1,1,1] => 206
[5,1,1,1,1,1,1] => 242
[4,4,3] => 146
[4,4,2,1] => 155
[4,4,1,1,1] => 170
[4,3,3,1] => 151
[4,3,2,2] => 155
[4,3,2,1,1] => 167
[4,3,1,1,1,1] => 191
[4,2,2,2,1] => 170
[4,2,2,1,1,1] => 191
[4,2,1,1,1,1,1] => 226
[4,1,1,1,1,1,1,1] => 275
[3,3,3,2] => 146
[3,3,3,1,1] => 158
[3,3,2,2,1] => 162
[3,3,2,1,1,1] => 183
[3,3,1,1,1,1,1] => 218
[3,2,2,2,2] => 170
[3,2,2,2,1,1] => 186
[3,2,2,1,1,1,1] => 218
[3,2,1,1,1,1,1,1] => 266
[3,1,1,1,1,1,1,1,1] => 330
[2,2,2,2,2,1] => 191
[2,2,2,2,1,1,1] => 218
[2,2,2,1,1,1,1,1] => 263
[2,2,1,1,1,1,1,1,1] => 326
[2,1,1,1,1,1,1,1,1,1] => 407
[1,1,1,1,1,1,1,1,1,1,1] => 506
[12] => 650
[11,1] => 530
[10,2] => 430
[10,1,1] => 434
[9,3] => 350
[9,2,1] => 353
[9,1,1,1] => 362
[8,4] => 290
[8,3,1] => 290
[8,2,2] => 290
[8,2,1,1] => 298
[8,1,1,1,1] => 314
[7,5] => 250
[7,4,1] => 245
[7,3,2] => 242
[7,3,1,1] => 250
[7,2,2,1] => 250
[7,2,1,1,1] => 265
[7,1,1,1,1,1] => 290
[6,6] => 230
[6,5,1] => 218
[6,4,2] => 210
[6,4,1,1] => 218
[6,3,3] => 206
[6,3,2,1] => 215
[6,3,1,1,1] => 230
[6,2,2,2] => 218
[6,2,2,1,1] => 230
[6,2,1,1,1,1] => 254
[6,1,1,1,1,1,1] => 290
[5,5,2] => 194
[5,5,1,1] => 202
[5,4,3] => 185
[5,4,2,1] => 194
[5,4,1,1,1] => 209
[5,3,3,1] => 190
[5,3,2,2] => 194
[5,3,2,1,1] => 206
[5,3,1,1,1,1] => 230
[5,2,2,2,1] => 209
[5,2,2,1,1,1] => 230
[5,2,1,1,1,1,1] => 265
[5,1,1,1,1,1,1,1] => 314
[4,4,4] => 170
[4,4,3,1] => 178
[4,4,2,2] => 182
[4,4,2,1,1] => 194
[4,4,1,1,1,1] => 218
[4,3,3,2] => 178
[4,3,3,1,1] => 190
[4,3,2,2,1] => 194
[4,3,2,1,1,1] => 215
[4,3,1,1,1,1,1] => 250
[4,2,2,2,2] => 202
[4,2,2,2,1,1] => 218
[4,2,2,1,1,1,1] => 250
[4,2,1,1,1,1,1,1] => 298
[4,1,1,1,1,1,1,1,1] => 362
[3,3,3,3] => 170
[3,3,3,2,1] => 185
[3,3,3,1,1,1] => 206
[3,3,2,2,2] => 194
[3,3,2,2,1,1] => 210
[3,3,2,1,1,1,1] => 242
[3,3,1,1,1,1,1,1] => 290
[3,2,2,2,2,1] => 218
[3,2,2,2,1,1,1] => 245
[3,2,2,1,1,1,1,1] => 290
[3,2,1,1,1,1,1,1,1] => 353
[3,1,1,1,1,1,1,1,1,1] => 434
[2,2,2,2,2,2] => 230
[2,2,2,2,2,1,1] => 250
[2,2,2,2,1,1,1,1] => 290
[2,2,2,1,1,1,1,1,1] => 350
[2,2,1,1,1,1,1,1,1,1] => 430
[2,1,1,1,1,1,1,1,1,1,1] => 530
[1,1,1,1,1,1,1,1,1,1,1,1] => 650
[13] => 819
[12,1] => 676
[11,2] => 555
[11,1,1] => 559
[10,3] => 456
[10,2,1] => 459
[10,1,1,1] => 468
[9,4] => 379
[9,3,1] => 379
[9,2,2] => 379
[9,2,1,1] => 387
[9,1,1,1,1] => 403
[8,5] => 324
[8,4,1] => 319
[8,3,2] => 316
[8,3,1,1] => 324
[8,2,2,1] => 324
[8,2,1,1,1] => 339
[8,1,1,1,1,1] => 364
[7,6] => 291
[7,5,1] => 279
[7,4,2] => 271
[7,4,1,1] => 279
[7,3,3] => 267
[7,3,2,1] => 276
[7,3,1,1,1] => 291
[7,2,2,2] => 279
[7,2,2,1,1] => 291
[7,2,1,1,1,1] => 315
[7,1,1,1,1,1,1] => 351
[6,6,1] => 259
[6,5,2] => 244
[6,5,1,1] => 252
[6,4,3] => 235
[6,4,2,1] => 244
[6,4,1,1,1] => 259
[6,3,3,1] => 240
[6,3,2,2] => 244
[6,3,2,1,1] => 256
[6,3,1,1,1,1] => 280
[6,2,2,2,1] => 259
[6,2,2,1,1,1] => 280
[6,2,1,1,1,1,1] => 315
[6,1,1,1,1,1,1,1] => 364
[5,5,3] => 219
[5,5,2,1] => 228
[5,5,1,1,1] => 243
[5,4,4] => 211
[5,4,3,1] => 219
[5,4,2,2] => 223
[5,4,2,1,1] => 235
[5,4,1,1,1,1] => 259
[5,3,3,2] => 219
[5,3,3,1,1] => 231
[5,3,2,2,1] => 235
[5,3,2,1,1,1] => 256
[5,3,1,1,1,1,1] => 291
[5,2,2,2,2] => 243
[5,2,2,2,1,1] => 259
[5,2,2,1,1,1,1] => 291
[5,2,1,1,1,1,1,1] => 339
[5,1,1,1,1,1,1,1,1] => 403
[4,4,4,1] => 204
[4,4,3,2] => 207
[4,4,3,1,1] => 219
[4,4,2,2,1] => 223
[4,4,2,1,1,1] => 244
[4,4,1,1,1,1,1] => 279
[4,3,3,3] => 204
[4,3,3,2,1] => 219
[4,3,3,1,1,1] => 240
[4,3,2,2,2] => 228
[4,3,2,2,1,1] => 244
[4,3,2,1,1,1,1] => 276
[4,3,1,1,1,1,1,1] => 324
[4,2,2,2,2,1] => 252
[4,2,2,2,1,1,1] => 279
[4,2,2,1,1,1,1,1] => 324
[4,2,1,1,1,1,1,1,1] => 387
[4,1,1,1,1,1,1,1,1,1] => 468
[3,3,3,3,1] => 211
[3,3,3,2,2] => 219
[3,3,3,2,1,1] => 235
[3,3,3,1,1,1,1] => 267
[3,3,2,2,2,1] => 244
[3,3,2,2,1,1,1] => 271
[3,3,2,1,1,1,1,1] => 316
[3,3,1,1,1,1,1,1,1] => 379
[3,2,2,2,2,2] => 259
[3,2,2,2,2,1,1] => 279
[3,2,2,2,1,1,1,1] => 319
[3,2,2,1,1,1,1,1,1] => 379
[3,2,1,1,1,1,1,1,1,1] => 459
[3,1,1,1,1,1,1,1,1,1,1] => 559
[2,2,2,2,2,2,1] => 291
[2,2,2,2,2,1,1,1] => 324
[2,2,2,2,1,1,1,1,1] => 379
[2,2,2,1,1,1,1,1,1,1] => 456
[2,2,1,1,1,1,1,1,1,1,1] => 555
[2,1,1,1,1,1,1,1,1,1,1,1] => 676
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 819
[14] => 1015
[13,1] => 847
[12,2] => 703
[12,1,1] => 707
[11,3] => 583
[11,2,1] => 586
[11,1,1,1] => 595
[10,4] => 487
[10,3,1] => 487
[10,2,2] => 487
[10,2,1,1] => 495
[10,1,1,1,1] => 511
[9,5] => 415
[9,4,1] => 410
[9,3,2] => 407
[9,3,1,1] => 415
[9,2,2,1] => 415
[9,2,1,1,1] => 430
[9,1,1,1,1,1] => 455
[8,6] => 367
[8,5,1] => 355
[8,4,2] => 347
[8,4,1,1] => 355
[8,3,3] => 343
[8,3,2,1] => 352
[8,3,1,1,1] => 367
[8,2,2,2] => 355
[8,2,2,1,1] => 367
[8,2,1,1,1,1] => 391
[8,1,1,1,1,1,1] => 427
[7,7] => 343
[7,6,1] => 322
[7,5,2] => 307
[7,5,1,1] => 315
[7,4,3] => 298
[7,4,2,1] => 307
[7,4,1,1,1] => 322
[7,3,3,1] => 303
[7,3,2,2] => 307
[7,3,2,1,1] => 319
[7,3,1,1,1,1] => 343
[7,2,2,2,1] => 322
[7,2,2,1,1,1] => 343
[7,2,1,1,1,1,1] => 378
[7,1,1,1,1,1,1,1] => 427
[6,6,2] => 287
[6,6,1,1] => 295
[6,5,3] => 271
[6,5,2,1] => 280
[6,5,1,1,1] => 295
[6,4,4] => 263
[6,4,3,1] => 271
[6,4,2,2] => 275
[6,4,2,1,1] => 287
[6,4,1,1,1,1] => 311
[6,3,3,2] => 271
[6,3,3,1,1] => 283
[6,3,2,2,1] => 287
[6,3,2,1,1,1] => 308
[6,3,1,1,1,1,1] => 343
[6,2,2,2,2] => 295
[6,2,2,2,1,1] => 311
[6,2,2,1,1,1,1] => 343
[6,2,1,1,1,1,1,1] => 391
[6,1,1,1,1,1,1,1,1] => 455
[5,5,4] => 247
[5,5,3,1] => 255
[5,5,2,2] => 259
[5,5,2,1,1] => 271
[5,5,1,1,1,1] => 295
[5,4,4,1] => 247
[5,4,3,2] => 250
[5,4,3,1,1] => 262
[5,4,2,2,1] => 266
[5,4,2,1,1,1] => 287
[5,4,1,1,1,1,1] => 322
[5,3,3,3] => 247
[5,3,3,2,1] => 262
[5,3,3,1,1,1] => 283
[5,3,2,2,2] => 271
[5,3,2,2,1,1] => 287
[5,3,2,1,1,1,1] => 319
[5,3,1,1,1,1,1,1] => 367
[5,2,2,2,2,1] => 295
[5,2,2,2,1,1,1] => 322
[5,2,2,1,1,1,1,1] => 367
[5,2,1,1,1,1,1,1,1] => 430
[5,1,1,1,1,1,1,1,1,1] => 511
[4,4,4,2] => 235
[4,4,4,1,1] => 247
[4,4,3,3] => 235
[4,4,3,2,1] => 250
[4,4,3,1,1,1] => 271
[4,4,2,2,2] => 259
[4,4,2,2,1,1] => 275
[4,4,2,1,1,1,1] => 307
[4,4,1,1,1,1,1,1] => 355
[4,3,3,3,1] => 247
[4,3,3,2,2] => 255
[4,3,3,2,1,1] => 271
[4,3,3,1,1,1,1] => 303
[4,3,2,2,2,1] => 280
[4,3,2,2,1,1,1] => 307
[4,3,2,1,1,1,1,1] => 352
[4,3,1,1,1,1,1,1,1] => 415
[4,2,2,2,2,2] => 295
[4,2,2,2,2,1,1] => 315
[4,2,2,2,1,1,1,1] => 355
[4,2,2,1,1,1,1,1,1] => 415
[4,2,1,1,1,1,1,1,1,1] => 495
[4,1,1,1,1,1,1,1,1,1,1] => 595
[3,3,3,3,2] => 247
[3,3,3,3,1,1] => 263
[3,3,3,2,2,1] => 271
[3,3,3,2,1,1,1] => 298
[3,3,3,1,1,1,1,1] => 343
[3,3,2,2,2,2] => 287
[3,3,2,2,2,1,1] => 307
[3,3,2,2,1,1,1,1] => 347
[3,3,2,1,1,1,1,1,1] => 407
[3,3,1,1,1,1,1,1,1,1] => 487
[3,2,2,2,2,2,1] => 322
[3,2,2,2,2,1,1,1] => 355
[3,2,2,2,1,1,1,1,1] => 410
[3,2,2,1,1,1,1,1,1,1] => 487
[3,2,1,1,1,1,1,1,1,1,1] => 586
[3,1,1,1,1,1,1,1,1,1,1,1] => 707
[2,2,2,2,2,2,2] => 343
[2,2,2,2,2,2,1,1] => 367
[2,2,2,2,2,1,1,1,1] => 415
[2,2,2,2,1,1,1,1,1,1] => 487
[2,2,2,1,1,1,1,1,1,1,1] => 583
[2,2,1,1,1,1,1,1,1,1,1,1] => 703
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 847
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1015
[15] => 1240
[14,1] => 1045
[13,2] => 876
[13,1,1] => 880
[12,3] => 733
[12,2,1] => 736
[12,1,1,1] => 745
[11,4] => 616
[11,3,1] => 616
[11,2,2] => 616
[11,2,1,1] => 624
[11,1,1,1,1] => 640
[10,5] => 525
[10,4,1] => 520
[10,3,2] => 517
[10,3,1,1] => 525
[10,2,2,1] => 525
[10,2,1,1,1] => 540
[10,1,1,1,1,1] => 565
[9,6] => 460
[9,5,1] => 448
[9,4,2] => 440
[9,4,1,1] => 448
[9,3,3] => 436
[9,3,2,1] => 445
[9,3,1,1,1] => 460
[9,2,2,2] => 448
[9,2,2,1,1] => 460
[9,2,1,1,1,1] => 484
[9,1,1,1,1,1,1] => 520
[8,7] => 421
[8,6,1] => 400
[8,5,2] => 385
[8,5,1,1] => 393
[8,4,3] => 376
[8,4,2,1] => 385
[8,4,1,1,1] => 400
[8,3,3,1] => 381
[8,3,2,2] => 385
[8,3,2,1,1] => 397
[8,3,1,1,1,1] => 421
[8,2,2,2,1] => 400
[8,2,2,1,1,1] => 421
[8,2,1,1,1,1,1] => 456
[8,1,1,1,1,1,1,1] => 505
[7,7,1] => 376
[7,6,2] => 352
[7,6,1,1] => 360
[7,5,3] => 336
[7,5,2,1] => 345
[7,5,1,1,1] => 360
[7,4,4] => 328
[7,4,3,1] => 336
[7,4,2,2] => 340
[7,4,2,1,1] => 352
[7,4,1,1,1,1] => 376
[7,3,3,2] => 336
[7,3,3,1,1] => 348
[7,3,2,2,1] => 352
[7,3,2,1,1,1] => 373
[7,3,1,1,1,1,1] => 408
[7,2,2,2,2] => 360
[7,2,2,2,1,1] => 376
[7,2,2,1,1,1,1] => 408
[7,2,1,1,1,1,1,1] => 456
[7,1,1,1,1,1,1,1,1] => 520
[6,6,3] => 316
[6,6,2,1] => 325
[6,6,1,1,1] => 340
[6,5,4] => 301
[6,5,3,1] => 309
[6,5,2,2] => 313
[6,5,2,1,1] => 325
[6,5,1,1,1,1] => 349
[6,4,4,1] => 301
[6,4,3,2] => 304
[6,4,3,1,1] => 316
[6,4,2,2,1] => 320
[6,4,2,1,1,1] => 341
[6,4,1,1,1,1,1] => 376
[6,3,3,3] => 301
[6,3,3,2,1] => 316
[6,3,3,1,1,1] => 337
[6,3,2,2,2] => 325
[6,3,2,2,1,1] => 341
[6,3,2,1,1,1,1] => 373
[6,3,1,1,1,1,1,1] => 421
[6,2,2,2,2,1] => 349
[6,2,2,2,1,1,1] => 376
[6,2,2,1,1,1,1,1] => 421
[6,2,1,1,1,1,1,1,1] => 484
[6,1,1,1,1,1,1,1,1,1] => 565
[5,5,5] => 280
[5,5,4,1] => 285
[5,5,3,2] => 288
[5,5,3,1,1] => 300
[5,5,2,2,1] => 304
[5,5,2,1,1,1] => 325
[5,5,1,1,1,1,1] => 360
[5,4,4,2] => 280
[5,4,4,1,1] => 292
[5,4,3,3] => 280
[5,4,3,2,1] => 295
[5,4,3,1,1,1] => 316
[5,4,2,2,2] => 304
[5,4,2,2,1,1] => 320
[5,4,2,1,1,1,1] => 352
[5,4,1,1,1,1,1,1] => 400
[5,3,3,3,1] => 292
[5,3,3,2,2] => 300
[5,3,3,2,1,1] => 316
[5,3,3,1,1,1,1] => 348
[5,3,2,2,2,1] => 325
[5,3,2,2,1,1,1] => 352
[5,3,2,1,1,1,1,1] => 397
[5,3,1,1,1,1,1,1,1] => 460
[5,2,2,2,2,2] => 340
[5,2,2,2,2,1,1] => 360
[5,2,2,2,1,1,1,1] => 400
[5,2,2,1,1,1,1,1,1] => 460
[5,2,1,1,1,1,1,1,1,1] => 540
[5,1,1,1,1,1,1,1,1,1,1] => 640
[4,4,4,3] => 265
[4,4,4,2,1] => 280
[4,4,4,1,1,1] => 301
[4,4,3,3,1] => 280
[4,4,3,2,2] => 288
[4,4,3,2,1,1] => 304
[4,4,3,1,1,1,1] => 336
[4,4,2,2,2,1] => 313
[4,4,2,2,1,1,1] => 340
[4,4,2,1,1,1,1,1] => 385
[4,4,1,1,1,1,1,1,1] => 448
[4,3,3,3,2] => 285
[4,3,3,3,1,1] => 301
[4,3,3,2,2,1] => 309
[4,3,3,2,1,1,1] => 336
[4,3,3,1,1,1,1,1] => 381
[4,3,2,2,2,2] => 325
[4,3,2,2,2,1,1] => 345
[4,3,2,2,1,1,1,1] => 385
[4,3,2,1,1,1,1,1,1] => 445
[4,3,1,1,1,1,1,1,1,1] => 525
[4,2,2,2,2,2,1] => 360
[4,2,2,2,2,1,1,1] => 393
[4,2,2,2,1,1,1,1,1] => 448
[4,2,2,1,1,1,1,1,1,1] => 525
[4,2,1,1,1,1,1,1,1,1,1] => 624
[4,1,1,1,1,1,1,1,1,1,1,1] => 745
[3,3,3,3,3] => 280
[3,3,3,3,2,1] => 301
[3,3,3,3,1,1,1] => 328
[3,3,3,2,2,2] => 316
[3,3,3,2,2,1,1] => 336
[3,3,3,2,1,1,1,1] => 376
[3,3,3,1,1,1,1,1,1] => 436
[3,3,2,2,2,2,1] => 352
[3,3,2,2,2,1,1,1] => 385
[3,3,2,2,1,1,1,1,1] => 440
[3,3,2,1,1,1,1,1,1,1] => 517
[3,3,1,1,1,1,1,1,1,1,1] => 616
[3,2,2,2,2,2,2] => 376
[3,2,2,2,2,2,1,1] => 400
[3,2,2,2,2,1,1,1,1] => 448
[3,2,2,2,1,1,1,1,1,1] => 520
[3,2,2,1,1,1,1,1,1,1,1] => 616
[3,2,1,1,1,1,1,1,1,1,1,1] => 736
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 880
[2,2,2,2,2,2,2,1] => 421
[2,2,2,2,2,2,1,1,1] => 460
[2,2,2,2,2,1,1,1,1,1] => 525
[2,2,2,2,1,1,1,1,1,1,1] => 616
[2,2,2,1,1,1,1,1,1,1,1,1] => 733
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 876
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1045
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1240
[16] => 1496
[15,1] => 1272
[14,2] => 1076
[14,1,1] => 1080
[13,3] => 908
[13,2,1] => 911
[13,1,1,1] => 920
[12,4] => 768
[12,3,1] => 768
[12,2,2] => 768
[12,2,1,1] => 776
[12,1,1,1,1] => 792
[11,5] => 656
[11,4,1] => 651
[11,3,2] => 648
[11,3,1,1] => 656
[11,2,2,1] => 656
[11,2,1,1,1] => 671
[11,1,1,1,1,1] => 696
[10,6] => 572
[10,5,1] => 560
[10,4,2] => 552
[10,4,1,1] => 560
[10,3,3] => 548
[10,3,2,1] => 557
[10,3,1,1,1] => 572
[10,2,2,2] => 560
[10,2,2,1,1] => 572
[10,2,1,1,1,1] => 596
[10,1,1,1,1,1,1] => 632
[9,7] => 516
[9,6,1] => 495
[9,5,2] => 480
[9,5,1,1] => 488
[9,4,3] => 471
[9,4,2,1] => 480
[9,4,1,1,1] => 495
[9,3,3,1] => 476
[9,3,2,2] => 480
[9,3,2,1,1] => 492
[9,3,1,1,1,1] => 516
[9,2,2,2,1] => 495
[9,2,2,1,1,1] => 516
[9,2,1,1,1,1,1] => 551
[9,1,1,1,1,1,1,1] => 600
[8,8] => 488
[8,7,1] => 456
[8,6,2] => 432
[8,6,1,1] => 440
[8,5,3] => 416
[8,5,2,1] => 425
[8,5,1,1,1] => 440
[8,4,4] => 408
[8,4,3,1] => 416
[8,4,2,2] => 420
[8,4,2,1,1] => 432
[8,4,1,1,1,1] => 456
[8,3,3,2] => 416
[8,3,3,1,1] => 428
[8,3,2,2,1] => 432
[8,3,2,1,1,1] => 453
[8,3,1,1,1,1,1] => 488
[8,2,2,2,2] => 440
[8,2,2,2,1,1] => 456
[8,2,2,1,1,1,1] => 488
[8,2,1,1,1,1,1,1] => 536
[8,1,1,1,1,1,1,1,1] => 600
[7,7,2] => 408
[7,7,1,1] => 416
[7,6,3] => 383
[7,6,2,1] => 392
[7,6,1,1,1] => 407
[7,5,4] => 368
[7,5,3,1] => 376
[7,5,2,2] => 380
[7,5,2,1,1] => 392
[7,5,1,1,1,1] => 416
[7,4,4,1] => 368
[7,4,3,2] => 371
[7,4,3,1,1] => 383
[7,4,2,2,1] => 387
[7,4,2,1,1,1] => 408
[7,4,1,1,1,1,1] => 443
[7,3,3,3] => 368
[7,3,3,2,1] => 383
[7,3,3,1,1,1] => 404
[7,3,2,2,2] => 392
[7,3,2,2,1,1] => 408
[7,3,2,1,1,1,1] => 440
[7,3,1,1,1,1,1,1] => 488
[7,2,2,2,2,1] => 416
[7,2,2,2,1,1,1] => 443
[7,2,2,1,1,1,1,1] => 488
[7,2,1,1,1,1,1,1,1] => 551
[7,1,1,1,1,1,1,1,1,1] => 632
[6,6,4] => 348
[6,6,3,1] => 356
[6,6,2,2] => 360
[6,6,2,1,1] => 372
[6,6,1,1,1,1] => 396
[6,5,5] => 336
[6,5,4,1] => 341
[6,5,3,2] => 344
[6,5,3,1,1] => 356
[6,5,2,2,1] => 360
[6,5,2,1,1,1] => 381
[6,5,1,1,1,1,1] => 416
[6,4,4,2] => 336
[6,4,4,1,1] => 348
[6,4,3,3] => 336
[6,4,3,2,1] => 351
[6,4,3,1,1,1] => 372
[6,4,2,2,2] => 360
[6,4,2,2,1,1] => 376
[6,4,2,1,1,1,1] => 408
[6,4,1,1,1,1,1,1] => 456
[6,3,3,3,1] => 348
[6,3,3,2,2] => 356
[6,3,3,2,1,1] => 372
[6,3,3,1,1,1,1] => 404
[6,3,2,2,2,1] => 381
[6,3,2,2,1,1,1] => 408
[6,3,2,1,1,1,1,1] => 453
[6,3,1,1,1,1,1,1,1] => 516
[6,2,2,2,2,2] => 396
[6,2,2,2,2,1,1] => 416
[6,2,2,2,1,1,1,1] => 456
[6,2,2,1,1,1,1,1,1] => 516
[6,2,1,1,1,1,1,1,1,1] => 596
[6,1,1,1,1,1,1,1,1,1,1] => 696
[5,5,5,1] => 320
[5,5,4,2] => 320
[5,5,4,1,1] => 332
[5,5,3,3] => 320
[5,5,3,2,1] => 335
[5,5,3,1,1,1] => 356
[5,5,2,2,2] => 344
[5,5,2,2,1,1] => 360
[5,5,2,1,1,1,1] => 392
[5,5,1,1,1,1,1,1] => 440
[5,4,4,3] => 312
[5,4,4,2,1] => 327
[5,4,4,1,1,1] => 348
[5,4,3,3,1] => 327
[5,4,3,2,2] => 335
[5,4,3,2,1,1] => 351
[5,4,3,1,1,1,1] => 383
[5,4,2,2,2,1] => 360
[5,4,2,2,1,1,1] => 387
[5,4,2,1,1,1,1,1] => 432
[5,4,1,1,1,1,1,1,1] => 495
[5,3,3,3,2] => 332
[5,3,3,3,1,1] => 348
[5,3,3,2,2,1] => 356
[5,3,3,2,1,1,1] => 383
[5,3,3,1,1,1,1,1] => 428
[5,3,2,2,2,2] => 372
[5,3,2,2,2,1,1] => 392
[5,3,2,2,1,1,1,1] => 432
[5,3,2,1,1,1,1,1,1] => 492
[5,3,1,1,1,1,1,1,1,1] => 572
[5,2,2,2,2,2,1] => 407
[5,2,2,2,2,1,1,1] => 440
[5,2,2,2,1,1,1,1,1] => 495
[5,2,2,1,1,1,1,1,1,1] => 572
[5,2,1,1,1,1,1,1,1,1,1] => 671
[5,1,1,1,1,1,1,1,1,1,1,1] => 792
[4,4,4,4] => 296
[4,4,4,3,1] => 312
[4,4,4,2,2] => 320
[4,4,4,2,1,1] => 336
[4,4,4,1,1,1,1] => 368
[4,4,3,3,2] => 320
[4,4,3,3,1,1] => 336
[4,4,3,2,2,1] => 344
[4,4,3,2,1,1,1] => 371
[4,4,3,1,1,1,1,1] => 416
[4,4,2,2,2,2] => 360
[4,4,2,2,2,1,1] => 380
[4,4,2,2,1,1,1,1] => 420
[4,4,2,1,1,1,1,1,1] => 480
[4,4,1,1,1,1,1,1,1,1] => 560
[4,3,3,3,3] => 320
[4,3,3,3,2,1] => 341
[4,3,3,3,1,1,1] => 368
[4,3,3,2,2,2] => 356
[4,3,3,2,2,1,1] => 376
[4,3,3,2,1,1,1,1] => 416
[4,3,3,1,1,1,1,1,1] => 476
[4,3,2,2,2,2,1] => 392
[4,3,2,2,2,1,1,1] => 425
[4,3,2,2,1,1,1,1,1] => 480
[4,3,2,1,1,1,1,1,1,1] => 557
[4,3,1,1,1,1,1,1,1,1,1] => 656
[4,2,2,2,2,2,2] => 416
[4,2,2,2,2,2,1,1] => 440
[4,2,2,2,2,1,1,1,1] => 488
[4,2,2,2,1,1,1,1,1,1] => 560
[4,2,2,1,1,1,1,1,1,1,1] => 656
[4,2,1,1,1,1,1,1,1,1,1,1] => 776
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 920
[3,3,3,3,3,1] => 336
[3,3,3,3,2,2] => 348
[3,3,3,3,2,1,1] => 368
[3,3,3,3,1,1,1,1] => 408
[3,3,3,2,2,2,1] => 383
[3,3,3,2,2,1,1,1] => 416
[3,3,3,2,1,1,1,1,1] => 471
[3,3,3,1,1,1,1,1,1,1] => 548
[3,3,2,2,2,2,2] => 408
[3,3,2,2,2,2,1,1] => 432
[3,3,2,2,2,1,1,1,1] => 480
[3,3,2,2,1,1,1,1,1,1] => 552
[3,3,2,1,1,1,1,1,1,1,1] => 648
[3,3,1,1,1,1,1,1,1,1,1,1] => 768
[3,2,2,2,2,2,2,1] => 456
[3,2,2,2,2,2,1,1,1] => 495
[3,2,2,2,2,1,1,1,1,1] => 560
[3,2,2,2,1,1,1,1,1,1,1] => 651
[3,2,2,1,1,1,1,1,1,1,1,1] => 768
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 911
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1080
[2,2,2,2,2,2,2,2] => 488
[2,2,2,2,2,2,2,1,1] => 516
[2,2,2,2,2,2,1,1,1,1] => 572
[2,2,2,2,2,1,1,1,1,1,1] => 656
[2,2,2,2,1,1,1,1,1,1,1,1] => 768
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 908
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 1076
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1272
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1496
[17] => 1785
[16,1] => 1530
[15,2] => 1305
[15,1,1] => 1309
[14,3] => 1110
[14,2,1] => 1113
[14,1,1,1] => 1122
[13,4] => 945
[13,3,1] => 945
[13,2,2] => 945
[13,2,1,1] => 953
[13,1,1,1,1] => 969
[12,5] => 810
[12,4,1] => 805
[12,3,2] => 802
[12,3,1,1] => 810
[12,2,2,1] => 810
[12,2,1,1,1] => 825
[12,1,1,1,1,1] => 850
[11,6] => 705
[11,5,1] => 693
[11,4,2] => 685
[11,4,1,1] => 693
[11,3,3] => 681
[11,3,2,1] => 690
[11,3,1,1,1] => 705
[11,2,2,2] => 693
[11,2,2,1,1] => 705
[11,2,1,1,1,1] => 729
[11,1,1,1,1,1,1] => 765
[10,7] => 630
[10,6,1] => 609
[10,5,2] => 594
[10,5,1,1] => 602
[10,4,3] => 585
[10,4,2,1] => 594
[10,4,1,1,1] => 609
[10,3,3,1] => 590
[10,3,2,2] => 594
[10,3,2,1,1] => 606
[10,3,1,1,1,1] => 630
[10,2,2,2,1] => 609
[10,2,2,1,1,1] => 630
[10,2,1,1,1,1,1] => 665
[10,1,1,1,1,1,1,1] => 714
[9,8] => 585
[9,7,1] => 553
[9,6,2] => 529
[9,6,1,1] => 537
[9,5,3] => 513
[9,5,2,1] => 522
[9,5,1,1,1] => 537
[9,4,4] => 505
[9,4,3,1] => 513
[9,4,2,2] => 517
[9,4,2,1,1] => 529
[9,4,1,1,1,1] => 553
[9,3,3,2] => 513
[9,3,3,1,1] => 525
[9,3,2,2,1] => 529
[9,3,2,1,1,1] => 550
[9,3,1,1,1,1,1] => 585
[9,2,2,2,2] => 537
[9,2,2,2,1,1] => 553
[9,2,2,1,1,1,1] => 585
[9,2,1,1,1,1,1,1] => 633
[9,1,1,1,1,1,1,1,1] => 697
[8,8,1] => 525
[8,7,2] => 490
[8,7,1,1] => 498
[8,6,3] => 465
[8,6,2,1] => 474
[8,6,1,1,1] => 489
[8,5,4] => 450
[8,5,3,1] => 458
[8,5,2,2] => 462
[8,5,2,1,1] => 474
[8,5,1,1,1,1] => 498
[8,4,4,1] => 450
[8,4,3,2] => 453
[8,4,3,1,1] => 465
[8,4,2,2,1] => 469
[8,4,2,1,1,1] => 490
[8,4,1,1,1,1,1] => 525
[8,3,3,3] => 450
[8,3,3,2,1] => 465
[8,3,3,1,1,1] => 486
[8,3,2,2,2] => 474
[8,3,2,2,1,1] => 490
[8,3,2,1,1,1,1] => 522
[8,3,1,1,1,1,1,1] => 570
[8,2,2,2,2,1] => 498
[8,2,2,2,1,1,1] => 525
[8,2,2,1,1,1,1,1] => 570
[8,2,1,1,1,1,1,1,1] => 633
[8,1,1,1,1,1,1,1,1,1] => 714
[7,7,3] => 441
[7,7,2,1] => 450
[7,7,1,1,1] => 465
[7,6,4] => 417
[7,6,3,1] => 425
[7,6,2,2] => 429
[7,6,2,1,1] => 441
[7,6,1,1,1,1] => 465
[7,5,5] => 405
[7,5,4,1] => 410
[7,5,3,2] => 413
[7,5,3,1,1] => 425
[7,5,2,2,1] => 429
[7,5,2,1,1,1] => 450
[7,5,1,1,1,1,1] => 485
[7,4,4,2] => 405
[7,4,4,1,1] => 417
[7,4,3,3] => 405
[7,4,3,2,1] => 420
[7,4,3,1,1,1] => 441
[7,4,2,2,2] => 429
[7,4,2,2,1,1] => 445
[7,4,2,1,1,1,1] => 477
[7,4,1,1,1,1,1,1] => 525
[7,3,3,3,1] => 417
[7,3,3,2,2] => 425
[7,3,3,2,1,1] => 441
[7,3,3,1,1,1,1] => 473
[7,3,2,2,2,1] => 450
[7,3,2,2,1,1,1] => 477
[7,3,2,1,1,1,1,1] => 522
[7,3,1,1,1,1,1,1,1] => 585
[7,2,2,2,2,2] => 465
[7,2,2,2,2,1,1] => 485
[7,2,2,2,1,1,1,1] => 525
[7,2,2,1,1,1,1,1,1] => 585
[7,2,1,1,1,1,1,1,1,1] => 665
[7,1,1,1,1,1,1,1,1,1,1] => 765
[6,6,5] => 385
[6,6,4,1] => 390
[6,6,3,2] => 393
[6,6,3,1,1] => 405
[6,6,2,2,1] => 409
[6,6,2,1,1,1] => 430
[6,6,1,1,1,1,1] => 465
[6,5,5,1] => 378
[6,5,4,2] => 378
[6,5,4,1,1] => 390
[6,5,3,3] => 378
[6,5,3,2,1] => 393
[6,5,3,1,1,1] => 414
[6,5,2,2,2] => 402
[6,5,2,2,1,1] => 418
[6,5,2,1,1,1,1] => 450
[6,5,1,1,1,1,1,1] => 498
[6,4,4,3] => 370
[6,4,4,2,1] => 385
[6,4,4,1,1,1] => 406
[6,4,3,3,1] => 385
[6,4,3,2,2] => 393
[6,4,3,2,1,1] => 409
[6,4,3,1,1,1,1] => 441
[6,4,2,2,2,1] => 418
[6,4,2,2,1,1,1] => 445
[6,4,2,1,1,1,1,1] => 490
[6,4,1,1,1,1,1,1,1] => 553
[6,3,3,3,2] => 390
[6,3,3,3,1,1] => 406
[6,3,3,2,2,1] => 414
[6,3,3,2,1,1,1] => 441
[6,3,3,1,1,1,1,1] => 486
[6,3,2,2,2,2] => 430
[6,3,2,2,2,1,1] => 450
[6,3,2,2,1,1,1,1] => 490
[6,3,2,1,1,1,1,1,1] => 550
[6,3,1,1,1,1,1,1,1,1] => 630
[6,2,2,2,2,2,1] => 465
[6,2,2,2,2,1,1,1] => 498
[6,2,2,2,1,1,1,1,1] => 553
[6,2,2,1,1,1,1,1,1,1] => 630
[6,2,1,1,1,1,1,1,1,1,1] => 729
[6,1,1,1,1,1,1,1,1,1,1,1] => 850
[5,5,5,2] => 357
[5,5,5,1,1] => 369
[5,5,4,3] => 354
[5,5,4,2,1] => 369
[5,5,4,1,1,1] => 390
[5,5,3,3,1] => 369
[5,5,3,2,2] => 377
[5,5,3,2,1,1] => 393
[5,5,3,1,1,1,1] => 425
[5,5,2,2,2,1] => 402
[5,5,2,2,1,1,1] => 429
[5,5,2,1,1,1,1,1] => 474
[5,5,1,1,1,1,1,1,1] => 537
[5,4,4,4] => 345
[5,4,4,3,1] => 361
[5,4,4,2,2] => 369
[5,4,4,2,1,1] => 385
[5,4,4,1,1,1,1] => 417
[5,4,3,3,2] => 369
[5,4,3,3,1,1] => 385
[5,4,3,2,2,1] => 393
[5,4,3,2,1,1,1] => 420
[5,4,3,1,1,1,1,1] => 465
[5,4,2,2,2,2] => 409
[5,4,2,2,2,1,1] => 429
[5,4,2,2,1,1,1,1] => 469
[5,4,2,1,1,1,1,1,1] => 529
[5,4,1,1,1,1,1,1,1,1] => 609
[5,3,3,3,3] => 369
[5,3,3,3,2,1] => 390
[5,3,3,3,1,1,1] => 417
[5,3,3,2,2,2] => 405
[5,3,3,2,2,1,1] => 425
[5,3,3,2,1,1,1,1] => 465
[5,3,3,1,1,1,1,1,1] => 525
[5,3,2,2,2,2,1] => 441
[5,3,2,2,2,1,1,1] => 474
[5,3,2,2,1,1,1,1,1] => 529
[5,3,2,1,1,1,1,1,1,1] => 606
[5,3,1,1,1,1,1,1,1,1,1] => 705
[5,2,2,2,2,2,2] => 465
[5,2,2,2,2,2,1,1] => 489
[5,2,2,2,2,1,1,1,1] => 537
[5,2,2,2,1,1,1,1,1,1] => 609
[5,2,2,1,1,1,1,1,1,1,1] => 705
[5,2,1,1,1,1,1,1,1,1,1,1] => 825
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 969
[4,4,4,4,1] => 345
[4,4,4,3,2] => 354
[4,4,4,3,1,1] => 370
[4,4,4,2,2,1] => 378
[4,4,4,2,1,1,1] => 405
[4,4,4,1,1,1,1,1] => 450
[4,4,3,3,3] => 357
[4,4,3,3,2,1] => 378
[4,4,3,3,1,1,1] => 405
[4,4,3,2,2,2] => 393
[4,4,3,2,2,1,1] => 413
[4,4,3,2,1,1,1,1] => 453
[4,4,3,1,1,1,1,1,1] => 513
[4,4,2,2,2,2,1] => 429
[4,4,2,2,2,1,1,1] => 462
[4,4,2,2,1,1,1,1,1] => 517
[4,4,2,1,1,1,1,1,1,1] => 594
[4,4,1,1,1,1,1,1,1,1,1] => 693
[4,3,3,3,3,1] => 378
[4,3,3,3,2,2] => 390
[4,3,3,3,2,1,1] => 410
[4,3,3,3,1,1,1,1] => 450
[4,3,3,2,2,2,1] => 425
[4,3,3,2,2,1,1,1] => 458
[4,3,3,2,1,1,1,1,1] => 513
[4,3,3,1,1,1,1,1,1,1] => 590
[4,3,2,2,2,2,2] => 450
[4,3,2,2,2,2,1,1] => 474
[4,3,2,2,2,1,1,1,1] => 522
[4,3,2,2,1,1,1,1,1,1] => 594
[4,3,2,1,1,1,1,1,1,1,1] => 690
[4,3,1,1,1,1,1,1,1,1,1,1] => 810
[4,2,2,2,2,2,2,1] => 498
[4,2,2,2,2,2,1,1,1] => 537
[4,2,2,2,2,1,1,1,1,1] => 602
[4,2,2,2,1,1,1,1,1,1,1] => 693
[4,2,2,1,1,1,1,1,1,1,1,1] => 810
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 953
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1122
[3,3,3,3,3,2] => 385
[3,3,3,3,3,1,1] => 405
[3,3,3,3,2,2,1] => 417
[3,3,3,3,2,1,1,1] => 450
[3,3,3,3,1,1,1,1,1] => 505
[3,3,3,2,2,2,2] => 441
[3,3,3,2,2,2,1,1] => 465
[3,3,3,2,2,1,1,1,1] => 513
[3,3,3,2,1,1,1,1,1,1] => 585
[3,3,3,1,1,1,1,1,1,1,1] => 681
[3,3,2,2,2,2,2,1] => 490
[3,3,2,2,2,2,1,1,1] => 529
[3,3,2,2,2,1,1,1,1,1] => 594
[3,3,2,2,1,1,1,1,1,1,1] => 685
[3,3,2,1,1,1,1,1,1,1,1,1] => 802
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 945
[3,2,2,2,2,2,2,2] => 525
[3,2,2,2,2,2,2,1,1] => 553
[3,2,2,2,2,2,1,1,1,1] => 609
[3,2,2,2,2,1,1,1,1,1,1] => 693
[3,2,2,2,1,1,1,1,1,1,1,1] => 805
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 945
-----------------------------------------------------------------------------
Created: Mar 11, 2024 at 11:27 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Mar 11, 2024 at 11:27 by Martin Rubey