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* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* 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. *
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-----------------------------------------------------------------------------
Statistic identifier: St001360
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The number of covering relations in Young's lattice below a partition.
-----------------------------------------------------------------------------
References: [1] Hopkins, S. Formula for number of edges in Hasse diagram of Young's lattice interval [[MathOverflow:324546]]
-----------------------------------------------------------------------------
Code:
@cached_function
def YoungsLattice(n):
return posets.YoungsLattice(n)
def statistic(la):
Y = YoungsLattice(la.size())
return len(Y.subposet(Y.principal_order_ideal(la)).cover_relations())
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 2
[1,1] => 2
[3] => 3
[2,1] => 5
[1,1,1] => 3
[4] => 4
[3,1] => 8
[2,2] => 6
[2,1,1] => 8
[1,1,1,1] => 4
[5] => 5
[4,1] => 11
[3,2] => 11
[3,1,1] => 13
[2,2,1] => 11
[2,1,1,1] => 11
[1,1,1,1,1] => 5
[6] => 6
[5,1] => 14
[4,2] => 16
[4,1,1] => 18
[3,3] => 12
[3,2,1] => 21
[3,1,1,1] => 18
[2,2,2] => 12
[2,2,1,1] => 16
[2,1,1,1,1] => 14
[1,1,1,1,1,1] => 6
[7] => 7
[6,1] => 17
[5,2] => 21
[5,1,1] => 23
[4,3] => 19
[4,2,1] => 31
[4,1,1,1] => 25
[3,3,1] => 24
[3,2,2] => 24
[3,2,1,1] => 31
[3,1,1,1,1] => 23
[2,2,2,1] => 19
[2,2,1,1,1] => 21
[2,1,1,1,1,1] => 17
[1,1,1,1,1,1,1] => 7
[8] => 8
[7,1] => 20
[6,2] => 26
[6,1,1] => 28
[5,3] => 26
[5,2,1] => 41
[5,1,1,1] => 32
[4,4] => 20
[4,3,1] => 39
[4,2,2] => 36
[4,2,1,1] => 46
[4,1,1,1,1] => 32
[3,3,2] => 29
[3,3,1,1] => 36
[3,2,2,1] => 39
[3,2,1,1,1] => 41
[3,1,1,1,1,1] => 28
[2,2,2,2] => 20
[2,2,2,1,1] => 26
[2,2,1,1,1,1] => 26
[2,1,1,1,1,1,1] => 20
[1,1,1,1,1,1,1,1] => 8
[9] => 9
[8,1] => 23
[7,2] => 31
[7,1,1] => 33
[6,3] => 33
[6,2,1] => 51
[6,1,1,1] => 39
[5,4] => 29
[5,3,1] => 54
[5,2,2] => 48
[5,2,1,1] => 61
[5,1,1,1,1] => 41
[4,4,1] => 42
[4,3,2] => 49
[4,3,1,1] => 59
[4,2,2,1] => 59
[4,2,1,1,1] => 61
[4,1,1,1,1,1] => 39
[3,3,3] => 30
[3,3,2,1] => 49
[3,3,1,1,1] => 48
[3,2,2,2] => 42
[3,2,2,1,1] => 54
[3,2,1,1,1,1] => 51
[3,1,1,1,1,1,1] => 33
[2,2,2,2,1] => 29
[2,2,2,1,1,1] => 33
[2,2,1,1,1,1,1] => 31
[2,1,1,1,1,1,1,1] => 23
[1,1,1,1,1,1,1,1,1] => 9
[10] => 10
[9,1] => 26
[8,2] => 36
[8,1,1] => 38
[7,3] => 40
[7,2,1] => 61
[7,1,1,1] => 46
[6,4] => 38
[6,3,1] => 69
[6,2,2] => 60
[6,2,1,1] => 76
[6,1,1,1,1] => 50
[5,5] => 30
[5,4,1] => 62
[5,3,2] => 69
[5,3,1,1] => 82
[5,2,2,1] => 79
[5,2,1,1,1] => 81
[5,1,1,1,1,1] => 50
[4,4,2] => 54
[4,4,1,1] => 64
[4,3,3] => 52
[4,3,2,1] => 84
[4,3,1,1,1] => 79
[4,2,2,2] => 64
[4,2,2,1,1] => 82
[4,2,1,1,1,1] => 76
[4,1,1,1,1,1,1] => 46
[3,3,3,1] => 52
[3,3,2,2] => 54
[3,3,2,1,1] => 69
[3,3,1,1,1,1] => 60
[3,2,2,2,1] => 62
[3,2,2,1,1,1] => 69
[3,2,1,1,1,1,1] => 61
[3,1,1,1,1,1,1,1] => 38
[2,2,2,2,2] => 30
[2,2,2,2,1,1] => 38
[2,2,2,1,1,1,1] => 40
[2,2,1,1,1,1,1,1] => 36
[2,1,1,1,1,1,1,1,1] => 26
[1,1,1,1,1,1,1,1,1,1] => 10
[11] => 11
[10,1] => 29
[9,2] => 41
[9,1,1] => 43
[8,3] => 47
[8,2,1] => 71
[8,1,1,1] => 53
[7,4] => 47
[7,3,1] => 84
[7,2,2] => 72
[7,2,1,1] => 91
[7,1,1,1,1] => 59
[6,5] => 41
[6,4,1] => 82
[6,3,2] => 89
[6,3,1,1] => 105
[6,2,2,1] => 99
[6,2,1,1,1] => 101
[6,1,1,1,1,1] => 61
[5,5,1] => 65
[5,4,2] => 82
[5,4,1,1] => 95
[5,3,3] => 74
[5,3,2,1] => 119
[5,3,1,1,1] => 110
[5,2,2,2] => 86
[5,2,2,1,1] => 110
[5,2,1,1,1,1] => 101
[5,1,1,1,1,1,1] => 59
[4,4,3] => 59
[4,4,2,1] => 94
[4,4,1,1,1] => 86
[4,3,3,1] => 92
[4,3,2,2] => 94
[4,3,2,1,1] => 119
[4,3,1,1,1,1] => 99
[4,2,2,2,1] => 95
[4,2,2,1,1,1] => 105
[4,2,1,1,1,1,1] => 91
[4,1,1,1,1,1,1,1] => 53
[3,3,3,2] => 59
[3,3,3,1,1] => 74
[3,3,2,2,1] => 82
[3,3,2,1,1,1] => 89
[3,3,1,1,1,1,1] => 72
[3,2,2,2,2] => 65
[3,2,2,2,1,1] => 82
[3,2,2,1,1,1,1] => 84
[3,2,1,1,1,1,1,1] => 71
[3,1,1,1,1,1,1,1,1] => 43
[2,2,2,2,2,1] => 41
[2,2,2,2,1,1,1] => 47
[2,2,2,1,1,1,1,1] => 47
[2,2,1,1,1,1,1,1,1] => 41
[2,1,1,1,1,1,1,1,1,1] => 29
[1,1,1,1,1,1,1,1,1,1,1] => 11
[12] => 12
[11,1] => 32
[10,2] => 46
[10,1,1] => 48
[9,3] => 54
[9,2,1] => 81
[9,1,1,1] => 60
[8,4] => 56
[8,3,1] => 99
[8,2,2] => 84
[8,2,1,1] => 106
[8,1,1,1,1] => 68
[7,5] => 52
[7,4,1] => 102
[7,3,2] => 109
[7,3,1,1] => 128
[7,2,2,1] => 119
[7,2,1,1,1] => 121
[7,1,1,1,1,1] => 72
[6,6] => 42
[6,5,1] => 90
[6,4,2] => 110
[6,4,1,1] => 126
[6,3,3] => 96
[6,3,2,1] => 154
[6,3,1,1,1] => 141
[6,2,2,2] => 108
[6,2,2,1,1] => 138
[6,2,1,1,1,1] => 126
[6,1,1,1,1,1,1] => 72
[5,5,2] => 87
[5,5,1,1] => 100
[5,4,3] => 92
[5,4,2,1] => 144
[5,4,1,1,1] => 128
[5,3,3,1] => 132
[5,3,2,2] => 134
[5,3,2,1,1] => 169
[5,3,1,1,1,1] => 138
[5,2,2,2,1] => 128
[5,2,2,1,1,1] => 141
[5,2,1,1,1,1,1] => 121
[5,1,1,1,1,1,1,1] => 68
[4,4,4] => 60
[4,4,3,1] => 107
[4,4,2,2] => 106
[4,4,2,1,1] => 134
[4,4,1,1,1,1] => 108
[4,3,3,2] => 107
[4,3,3,1,1] => 132
[4,3,2,2,1] => 144
[4,3,2,1,1,1] => 154
[4,3,1,1,1,1,1] => 119
[4,2,2,2,2] => 100
[4,2,2,2,1,1] => 126
[4,2,2,1,1,1,1] => 128
[4,2,1,1,1,1,1,1] => 106
[4,1,1,1,1,1,1,1,1] => 60
[3,3,3,3] => 60
[3,3,3,2,1] => 92
[3,3,3,1,1,1] => 96
[3,3,2,2,2] => 87
[3,3,2,2,1,1] => 110
[3,3,2,1,1,1,1] => 109
[3,3,1,1,1,1,1,1] => 84
[3,2,2,2,2,1] => 90
[3,2,2,2,1,1,1] => 102
[3,2,2,1,1,1,1,1] => 99
[3,2,1,1,1,1,1,1,1] => 81
[3,1,1,1,1,1,1,1,1,1] => 48
[2,2,2,2,2,2] => 42
[2,2,2,2,2,1,1] => 52
[2,2,2,2,1,1,1,1] => 56
[2,2,2,1,1,1,1,1,1] => 54
[2,2,1,1,1,1,1,1,1,1] => 46
[2,1,1,1,1,1,1,1,1,1,1] => 32
[1,1,1,1,1,1,1,1,1,1,1,1] => 12
[13] => 13
[12,1] => 35
[11,2] => 51
[11,1,1] => 53
[10,3] => 61
[10,2,1] => 91
[10,1,1,1] => 67
[9,4] => 65
[9,3,1] => 114
[9,2,2] => 96
[9,2,1,1] => 121
[9,1,1,1,1] => 77
[8,5] => 63
[8,4,1] => 122
[8,3,2] => 129
[8,3,1,1] => 151
[8,2,2,1] => 139
[8,2,1,1,1] => 141
[8,1,1,1,1,1] => 83
[7,6] => 55
[7,5,1] => 115
[7,4,2] => 138
[7,4,1,1] => 157
[7,3,3] => 118
[7,3,2,1] => 189
[7,3,1,1,1] => 172
[7,2,2,2] => 130
[7,2,2,1,1] => 166
[7,2,1,1,1,1] => 151
[7,1,1,1,1,1,1] => 85
[6,6,1] => 93
[6,5,2] => 123
[6,5,1,1] => 139
[6,4,3] => 125
[6,4,2,1] => 194
[6,4,1,1,1] => 170
[6,3,3,1] => 172
[6,3,2,2] => 174
[6,3,2,1,1] => 219
[6,3,1,1,1,1] => 177
[6,2,2,2,1] => 161
[6,2,2,1,1,1] => 177
[6,2,1,1,1,1,1] => 151
[6,1,1,1,1,1,1,1] => 83
[5,5,3] => 99
[5,5,2,1] => 154
[5,5,1,1,1] => 135
[5,4,4] => 95
[5,4,3,1] => 169
[5,4,2,2] => 164
[5,4,2,1,1] => 206
[5,4,1,1,1,1] => 161
[5,3,3,2] => 155
[5,3,3,1,1] => 190
[5,3,2,2,1] => 206
[5,3,2,1,1,1] => 219
[5,3,1,1,1,1,1] => 166
[5,2,2,2,2] => 135
[5,2,2,2,1,1] => 170
[5,2,2,1,1,1,1] => 172
[5,2,1,1,1,1,1,1] => 141
[5,1,1,1,1,1,1,1,1] => 77
[4,4,4,1] => 110
[4,4,3,2] => 127
[4,4,3,1,1] => 155
[4,4,2,2,1] => 164
[4,4,2,1,1,1] => 174
[4,4,1,1,1,1,1] => 130
[4,3,3,3] => 110
[4,3,3,2,1] => 169
[4,3,3,1,1,1] => 172
[4,3,2,2,2] => 154
[4,3,2,2,1,1] => 194
[4,3,2,1,1,1,1] => 189
[4,3,1,1,1,1,1,1] => 139
[4,2,2,2,2,1] => 139
[4,2,2,2,1,1,1] => 157
[4,2,2,1,1,1,1,1] => 151
[4,2,1,1,1,1,1,1,1] => 121
[4,1,1,1,1,1,1,1,1,1] => 67
[3,3,3,3,1] => 95
[3,3,3,2,2] => 99
[3,3,3,2,1,1] => 125
[3,3,3,1,1,1,1] => 118
[3,3,2,2,2,1] => 123
[3,3,2,2,1,1,1] => 138
[3,3,2,1,1,1,1,1] => 129
[3,3,1,1,1,1,1,1,1] => 96
[3,2,2,2,2,2] => 93
[3,2,2,2,2,1,1] => 115
[3,2,2,2,1,1,1,1] => 122
[3,2,2,1,1,1,1,1,1] => 114
[3,2,1,1,1,1,1,1,1,1] => 91
[3,1,1,1,1,1,1,1,1,1,1] => 53
[2,2,2,2,2,2,1] => 55
[2,2,2,2,2,1,1,1] => 63
[2,2,2,2,1,1,1,1,1] => 65
[2,2,2,1,1,1,1,1,1,1] => 61
[2,2,1,1,1,1,1,1,1,1,1] => 51
[2,1,1,1,1,1,1,1,1,1,1,1] => 35
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 13
[14] => 14
[13,1] => 38
[12,2] => 56
[12,1,1] => 58
[11,3] => 68
[11,2,1] => 101
[11,1,1,1] => 74
[10,4] => 74
[10,3,1] => 129
[10,2,2] => 108
[10,2,1,1] => 136
[10,1,1,1,1] => 86
[9,5] => 74
[9,4,1] => 142
[9,3,2] => 149
[9,3,1,1] => 174
[9,2,2,1] => 159
[9,2,1,1,1] => 161
[9,1,1,1,1,1] => 94
[8,6] => 68
[8,5,1] => 140
[8,4,2] => 166
[8,4,1,1] => 188
[8,3,3] => 140
[8,3,2,1] => 224
[8,3,1,1,1] => 203
[8,2,2,2] => 152
[8,2,2,1,1] => 194
[8,2,1,1,1,1] => 176
[8,1,1,1,1,1,1] => 98
[7,7] => 56
[7,6,1] => 123
[7,5,2] => 159
[7,5,1,1] => 178
[7,4,3] => 158
[7,4,2,1] => 244
[7,4,1,1,1] => 212
[7,3,3,1] => 212
[7,3,2,2] => 214
[7,3,2,1,1] => 269
[7,3,1,1,1,1] => 216
[7,2,2,2,1] => 194
[7,2,2,1,1,1] => 213
[7,2,1,1,1,1,1] => 181
[7,1,1,1,1,1,1,1] => 98
[6,6,2] => 128
[6,6,1,1] => 144
[6,5,3] => 143
[6,5,2,1] => 219
[6,5,1,1,1] => 188
[6,4,4] => 130
[6,4,3,1] => 231
[6,4,2,2] => 222
[6,4,2,1,1] => 278
[6,4,1,1,1,1] => 214
[6,3,3,2] => 203
[6,3,3,1,1] => 248
[6,3,2,2,1] => 268
[6,3,2,1,1,1] => 284
[6,3,1,1,1,1,1] => 213
[6,2,2,2,2] => 170
[6,2,2,2,1,1] => 214
[6,2,2,1,1,1,1] => 216
[6,2,1,1,1,1,1,1] => 176
[6,1,1,1,1,1,1,1,1] => 94
[5,5,4] => 104
[5,5,3,1] => 184
[5,5,2,2] => 176
[5,5,2,1,1] => 221
[5,5,1,1,1,1] => 170
[5,4,4,1] => 177
[5,4,3,2] => 204
[5,4,3,1,1] => 246
[5,4,2,2,1] => 255
[5,4,2,1,1,1] => 268
[5,4,1,1,1,1,1] => 194
[5,3,3,3] => 160
[5,3,3,2,1] => 246
[5,3,3,1,1,1] => 248
[5,3,2,2,2] => 221
[5,3,2,2,1,1] => 278
[5,3,2,1,1,1,1] => 269
[5,3,1,1,1,1,1,1] => 194
[5,2,2,2,2,1] => 188
[5,2,2,2,1,1,1] => 212
[5,2,2,1,1,1,1,1] => 203
[5,2,1,1,1,1,1,1,1] => 161
[5,1,1,1,1,1,1,1,1,1] => 86
[4,4,4,2] => 132
[4,4,4,1,1] => 160
[4,4,3,3] => 132
[4,4,3,2,1] => 204
[4,4,3,1,1,1] => 203
[4,4,2,2,2] => 176
[4,4,2,2,1,1] => 222
[4,4,2,1,1,1,1] => 214
[4,4,1,1,1,1,1,1] => 152
[4,3,3,3,1] => 177
[4,3,3,2,2] => 184
[4,3,3,2,1,1] => 231
[4,3,3,1,1,1,1] => 212
[4,3,2,2,2,1] => 219
[4,3,2,2,1,1,1] => 244
[4,3,2,1,1,1,1,1] => 224
[4,3,1,1,1,1,1,1,1] => 159
[4,2,2,2,2,2] => 144
[4,2,2,2,2,1,1] => 178
[4,2,2,2,1,1,1,1] => 188
[4,2,2,1,1,1,1,1,1] => 174
[4,2,1,1,1,1,1,1,1,1] => 136
[4,1,1,1,1,1,1,1,1,1,1] => 74
[3,3,3,3,2] => 104
[3,3,3,3,1,1] => 130
[3,3,3,2,2,1] => 143
[3,3,3,2,1,1,1] => 158
[3,3,3,1,1,1,1,1] => 140
[3,3,2,2,2,2] => 128
[3,3,2,2,2,1,1] => 159
[3,3,2,2,1,1,1,1] => 166
[3,3,2,1,1,1,1,1,1] => 149
[3,3,1,1,1,1,1,1,1,1] => 108
[3,2,2,2,2,2,1] => 123
[3,2,2,2,2,1,1,1] => 140
[3,2,2,2,1,1,1,1,1] => 142
[3,2,2,1,1,1,1,1,1,1] => 129
[3,2,1,1,1,1,1,1,1,1,1] => 101
[3,1,1,1,1,1,1,1,1,1,1,1] => 58
[2,2,2,2,2,2,2] => 56
[2,2,2,2,2,2,1,1] => 68
[2,2,2,2,2,1,1,1,1] => 74
[2,2,2,2,1,1,1,1,1,1] => 74
[2,2,2,1,1,1,1,1,1,1,1] => 68
[2,2,1,1,1,1,1,1,1,1,1,1] => 56
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 38
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 14
[15] => 15
[14,1] => 41
[13,2] => 61
[13,1,1] => 63
[12,3] => 75
[12,2,1] => 111
[12,1,1,1] => 81
[11,4] => 83
[11,3,1] => 144
[11,2,2] => 120
[11,2,1,1] => 151
[11,1,1,1,1] => 95
[10,5] => 85
[10,4,1] => 162
[10,3,2] => 169
[10,3,1,1] => 197
[10,2,2,1] => 179
[10,2,1,1,1] => 181
[10,1,1,1,1,1] => 105
[9,6] => 81
[9,5,1] => 165
[9,4,2] => 194
[9,4,1,1] => 219
[9,3,3] => 162
[9,3,2,1] => 259
[9,3,1,1,1] => 234
[9,2,2,2] => 174
[9,2,2,1,1] => 222
[9,2,1,1,1,1] => 201
[9,1,1,1,1,1,1] => 111
[8,7] => 71
[8,6,1] => 153
[8,5,2] => 195
[8,5,1,1] => 217
[8,4,3] => 191
[8,4,2,1] => 294
[8,4,1,1,1] => 254
[8,3,3,1] => 252
[8,3,2,2] => 254
[8,3,2,1,1] => 319
[8,3,1,1,1,1] => 255
[8,2,2,2,1] => 227
[8,2,2,1,1,1] => 249
[8,2,1,1,1,1,1] => 211
[8,1,1,1,1,1,1,1] => 113
[7,7,1] => 126
[7,6,2] => 172
[7,6,1,1] => 191
[7,5,3] => 187
[7,5,2,1] => 284
[7,5,1,1,1] => 241
[7,4,4] => 165
[7,4,3,1] => 293
[7,4,2,2] => 280
[7,4,2,1,1] => 350
[7,4,1,1,1,1] => 267
[7,3,3,2] => 251
[7,3,3,1,1] => 306
[7,3,2,2,1] => 330
[7,3,2,1,1,1] => 349
[7,3,1,1,1,1,1] => 260
[7,2,2,2,2] => 205
[7,2,2,2,1,1] => 258
[7,2,2,1,1,1,1] => 260
[7,2,1,1,1,1,1,1] => 211
[7,1,1,1,1,1,1,1,1] => 111
[6,6,3] => 150
[6,6,2,1] => 229
[6,6,1,1,1] => 195
[6,5,4] => 153
[6,5,3,1] => 268
[6,5,2,2] => 252
[6,5,2,1,1] => 315
[6,5,1,1,1,1] => 237
[6,4,4,1] => 244
[6,4,3,2] => 281
[6,4,3,1,1] => 337
[6,4,2,2,1] => 346
[6,4,2,1,1,1] => 362
[6,4,1,1,1,1,1] => 258
[6,3,3,3] => 210
[6,3,3,2,1] => 323
[6,3,3,1,1,1] => 324
[6,3,2,2,2] => 288
[6,3,2,2,1,1] => 362
[6,3,2,1,1,1,1] => 349
[6,3,1,1,1,1,1,1] => 249
[6,2,2,2,2,1] => 237
[6,2,2,2,1,1,1] => 267
[6,2,2,1,1,1,1,1] => 255
[6,2,1,1,1,1,1,1,1] => 201
[6,1,1,1,1,1,1,1,1,1] => 105
[5,5,5] => 105
[5,5,4,1] => 197
[5,5,3,2] => 224
[5,5,3,1,1] => 269
[5,5,2,2,1] => 275
[5,5,2,1,1,1] => 288
[5,5,1,1,1,1,1] => 205
[5,4,4,2] => 217
[5,4,4,1,1] => 259
[5,4,3,3] => 214
[5,4,3,2,1] => 330
[5,4,3,1,1,1] => 323
[5,4,2,2,2] => 275
[5,4,2,2,1,1] => 346
[5,4,2,1,1,1,1] => 330
[5,4,1,1,1,1,1,1] => 227
[5,3,3,3,1] => 259
[5,3,3,2,2] => 269
[5,3,3,2,1,1] => 337
[5,3,3,1,1,1,1] => 306
[5,3,2,2,2,1] => 315
[5,3,2,2,1,1,1] => 350
[5,3,2,1,1,1,1,1] => 319
[5,3,1,1,1,1,1,1,1] => 222
[5,2,2,2,2,2] => 195
[5,2,2,2,2,1,1] => 241
[5,2,2,2,1,1,1,1] => 254
[5,2,2,1,1,1,1,1,1] => 234
[5,2,1,1,1,1,1,1,1,1] => 181
[5,1,1,1,1,1,1,1,1,1,1] => 95
[4,4,4,3] => 139
[4,4,4,2,1] => 214
[4,4,4,1,1,1] => 210
[4,4,3,3,1] => 217
[4,4,3,2,2] => 224
[4,4,3,2,1,1] => 281
[4,4,3,1,1,1,1] => 251
[4,4,2,2,2,1] => 252
[4,4,2,2,1,1,1] => 280
[4,4,2,1,1,1,1,1] => 254
[4,4,1,1,1,1,1,1,1] => 174
[4,3,3,3,2] => 197
[4,3,3,3,1,1] => 244
[4,3,3,2,2,1] => 268
[4,3,3,2,1,1,1] => 293
[4,3,3,1,1,1,1,1] => 252
[4,3,2,2,2,2] => 229
[4,3,2,2,2,1,1] => 284
[4,3,2,2,1,1,1,1] => 294
[4,3,2,1,1,1,1,1,1] => 259
[4,3,1,1,1,1,1,1,1,1] => 179
[4,2,2,2,2,2,1] => 191
[4,2,2,2,2,1,1,1] => 217
[4,2,2,2,1,1,1,1,1] => 219
[4,2,2,1,1,1,1,1,1,1] => 197
[4,2,1,1,1,1,1,1,1,1,1] => 151
[4,1,1,1,1,1,1,1,1,1,1,1] => 81
[3,3,3,3,3] => 105
[3,3,3,3,2,1] => 153
[3,3,3,3,1,1,1] => 165
[3,3,3,2,2,2] => 150
[3,3,3,2,2,1,1] => 187
[3,3,3,2,1,1,1,1] => 191
[3,3,3,1,1,1,1,1,1] => 162
[3,3,2,2,2,2,1] => 172
[3,3,2,2,2,1,1,1] => 195
[3,3,2,2,1,1,1,1,1] => 194
[3,3,2,1,1,1,1,1,1,1] => 169
[3,3,1,1,1,1,1,1,1,1,1] => 120
[3,2,2,2,2,2,2] => 126
[3,2,2,2,2,2,1,1] => 153
[3,2,2,2,2,1,1,1,1] => 165
[3,2,2,2,1,1,1,1,1,1] => 162
[3,2,2,1,1,1,1,1,1,1,1] => 144
[3,2,1,1,1,1,1,1,1,1,1,1] => 111
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 63
[2,2,2,2,2,2,2,1] => 71
[2,2,2,2,2,2,1,1,1] => 81
[2,2,2,2,2,1,1,1,1,1] => 85
[2,2,2,2,1,1,1,1,1,1,1] => 83
[2,2,2,1,1,1,1,1,1,1,1,1] => 75
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 61
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 41
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 15
[16] => 16
[15,1] => 44
[14,2] => 66
[14,1,1] => 68
[13,3] => 82
[13,2,1] => 121
[13,1,1,1] => 88
[12,4] => 92
[12,3,1] => 159
[12,2,2] => 132
[12,2,1,1] => 166
[12,1,1,1,1] => 104
[11,5] => 96
[11,4,1] => 182
[11,3,2] => 189
[11,3,1,1] => 220
[11,2,2,1] => 199
[11,2,1,1,1] => 201
[11,1,1,1,1,1] => 116
[10,6] => 94
[10,5,1] => 190
[10,4,2] => 222
[10,4,1,1] => 250
[10,3,3] => 184
[10,3,2,1] => 294
[10,3,1,1,1] => 265
[10,2,2,2] => 196
[10,2,2,1,1] => 250
[10,2,1,1,1,1] => 226
[10,1,1,1,1,1,1] => 124
[9,7] => 86
[9,6,1] => 183
[9,5,2] => 231
[9,5,1,1] => 256
[9,4,3] => 224
[9,4,2,1] => 344
[9,4,1,1,1] => 296
[9,3,3,1] => 292
[9,3,2,2] => 294
[9,3,2,1,1] => 369
[9,3,1,1,1,1] => 294
[9,2,2,2,1] => 260
[9,2,2,1,1,1] => 285
[9,2,1,1,1,1,1] => 241
[9,1,1,1,1,1,1,1] => 128
[8,8] => 72
[8,7,1] => 161
[8,6,2] => 216
[8,6,1,1] => 238
[8,5,3] => 231
[8,5,2,1] => 349
[8,5,1,1,1] => 294
[8,4,4] => 200
[8,4,3,1] => 355
[8,4,2,2] => 338
[8,4,2,1,1] => 422
[8,4,1,1,1,1] => 320
[8,3,3,2] => 299
[8,3,3,1,1] => 364
[8,3,2,2,1] => 392
[8,3,2,1,1,1] => 414
[8,3,1,1,1,1,1] => 307
[8,2,2,2,2] => 240
[8,2,2,2,1,1] => 302
[8,2,2,1,1,1,1] => 304
[8,2,1,1,1,1,1,1] => 246
[8,1,1,1,1,1,1,1,1] => 128
[7,7,2] => 177
[7,7,1,1] => 196
[7,6,3] => 205
[7,6,2,1] => 309
[7,6,1,1,1] => 259
[7,5,4] => 202
[7,5,3,1] => 352
[7,5,2,2] => 328
[7,5,2,1,1] => 409
[7,5,1,1,1,1] => 304
[7,4,4,1] => 311
[7,4,3,2] => 358
[7,4,3,1,1] => 428
[7,4,2,2,1] => 437
[7,4,2,1,1,1] => 456
[7,4,1,1,1,1,1] => 322
[7,3,3,3] => 260
[7,3,3,2,1] => 400
[7,3,3,1,1,1] => 400
[7,3,2,2,2] => 355
[7,3,2,2,1,1] => 446
[7,3,2,1,1,1,1] => 429
[7,3,1,1,1,1,1,1] => 304
[7,2,2,2,2,1] => 286
[7,2,2,2,1,1,1] => 322
[7,2,2,1,1,1,1,1] => 307
[7,2,1,1,1,1,1,1,1] => 241
[7,1,1,1,1,1,1,1,1,1] => 124
[6,6,4] => 162
[6,6,3,1] => 283
[6,6,2,2] => 264
[6,6,2,1,1] => 330
[6,6,1,1,1,1] => 246
[6,5,5] => 156
[6,5,4,1] => 293
[6,5,3,2] => 330
[6,5,3,1,1] => 393
[6,5,2,2,1] => 395
[6,5,2,1,1,1] => 411
[6,5,1,1,1,1,1] => 286
[6,4,4,2] => 302
[6,4,4,1,1] => 358
[6,4,3,3] => 296
[6,4,3,2,1] => 456
[6,4,3,1,1,1] => 443
[6,4,2,2,2] => 374
[6,4,2,2,1,1] => 470
[6,4,2,1,1,1,1] => 446
[6,4,1,1,1,1,1,1] => 302
[6,3,3,3,1] => 341
[6,3,3,2,2] => 354
[6,3,3,2,1,1] => 443
[6,3,3,1,1,1,1] => 400
[6,3,2,2,2,1] => 411
[6,3,2,2,1,1,1] => 456
[6,3,2,1,1,1,1,1] => 414
[6,3,1,1,1,1,1,1,1] => 285
[6,2,2,2,2,2] => 246
[6,2,2,2,2,1,1] => 304
[6,2,2,2,1,1,1,1] => 320
[6,2,2,1,1,1,1,1,1] => 294
[6,2,1,1,1,1,1,1,1,1] => 226
[6,1,1,1,1,1,1,1,1,1,1] => 116
[5,5,5,1] => 200
[5,5,4,2] => 245
[5,5,4,1,1] => 290
[5,5,3,3] => 236
[5,5,3,2,1] => 365
[5,5,3,1,1,1] => 354
[5,5,2,2,2] => 297
[5,5,2,2,1,1] => 374
[5,5,2,1,1,1,1] => 355
[5,5,1,1,1,1,1,1] => 240
[5,4,4,3] => 232
[5,4,4,2,1] => 355
[5,4,4,1,1,1] => 341
[5,4,3,3,1] => 355
[5,4,3,2,2] => 365
[5,4,3,2,1,1] => 456
[5,4,3,1,1,1,1] => 400
[5,4,2,2,2,1] => 395
[5,4,2,2,1,1,1] => 437
[5,4,2,1,1,1,1,1] => 392
[5,4,1,1,1,1,1,1,1] => 260
[5,3,3,3,2] => 290
[5,3,3,3,1,1] => 358
[5,3,3,2,2,1] => 393
[5,3,3,2,1,1,1] => 428
[5,3,3,1,1,1,1,1] => 364
[5,3,2,2,2,2] => 330
[5,3,2,2,2,1,1] => 409
[5,3,2,2,1,1,1,1] => 422
[5,3,2,1,1,1,1,1,1] => 369
[5,3,1,1,1,1,1,1,1,1] => 250
[5,2,2,2,2,2,1] => 259
[5,2,2,2,2,1,1,1] => 294
[5,2,2,2,1,1,1,1,1] => 296
[5,2,2,1,1,1,1,1,1,1] => 265
[5,2,1,1,1,1,1,1,1,1,1] => 201
[5,1,1,1,1,1,1,1,1,1,1,1] => 104
[4,4,4,4] => 140
[4,4,4,3,1] => 232
[4,4,4,2,2] => 236
[4,4,4,2,1,1] => 296
[4,4,4,1,1,1,1] => 260
[4,4,3,3,2] => 245
[4,4,3,3,1,1] => 302
[4,4,3,2,2,1] => 330
[4,4,3,2,1,1,1] => 358
[4,4,3,1,1,1,1,1] => 299
[4,4,2,2,2,2] => 264
[4,4,2,2,2,1,1] => 328
[4,4,2,2,1,1,1,1] => 338
[4,4,2,1,1,1,1,1,1] => 294
[4,4,1,1,1,1,1,1,1,1] => 196
[4,3,3,3,3] => 200
[4,3,3,3,2,1] => 293
[4,3,3,3,1,1,1] => 311
[4,3,3,2,2,2] => 283
[4,3,3,2,2,1,1] => 352
[4,3,3,2,1,1,1,1] => 355
[4,3,3,1,1,1,1,1,1] => 292
[4,3,2,2,2,2,1] => 309
[4,3,2,2,2,1,1,1] => 349
[4,3,2,2,1,1,1,1,1] => 344
[4,3,2,1,1,1,1,1,1,1] => 294
[4,3,1,1,1,1,1,1,1,1,1] => 199
[4,2,2,2,2,2,2] => 196
[4,2,2,2,2,2,1,1] => 238
[4,2,2,2,2,1,1,1,1] => 256
[4,2,2,2,1,1,1,1,1,1] => 250
[4,2,2,1,1,1,1,1,1,1,1] => 220
[4,2,1,1,1,1,1,1,1,1,1,1] => 166
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 88
[3,3,3,3,3,1] => 156
[3,3,3,3,2,2] => 162
[3,3,3,3,2,1,1] => 202
[3,3,3,3,1,1,1,1] => 200
[3,3,3,2,2,2,1] => 205
[3,3,3,2,2,1,1,1] => 231
[3,3,3,2,1,1,1,1,1] => 224
[3,3,3,1,1,1,1,1,1,1] => 184
[3,3,2,2,2,2,2] => 177
[3,3,2,2,2,2,1,1] => 216
[3,3,2,2,2,1,1,1,1] => 231
[3,3,2,2,1,1,1,1,1,1] => 222
[3,3,2,1,1,1,1,1,1,1,1] => 189
[3,3,1,1,1,1,1,1,1,1,1,1] => 132
[3,2,2,2,2,2,2,1] => 161
[3,2,2,2,2,2,1,1,1] => 183
[3,2,2,2,2,1,1,1,1,1] => 190
[3,2,2,2,1,1,1,1,1,1,1] => 182
[3,2,2,1,1,1,1,1,1,1,1,1] => 159
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 121
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 68
[2,2,2,2,2,2,2,2] => 72
[2,2,2,2,2,2,2,1,1] => 86
[2,2,2,2,2,2,1,1,1,1] => 94
[2,2,2,2,2,1,1,1,1,1,1] => 96
[2,2,2,2,1,1,1,1,1,1,1,1] => 92
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 82
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 66
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 44
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 16
[17] => 17
[16,1] => 47
[15,2] => 71
[15,1,1] => 73
[14,3] => 89
[14,2,1] => 131
[14,1,1,1] => 95
[13,4] => 101
[13,3,1] => 174
[13,2,2] => 144
[13,2,1,1] => 181
[13,1,1,1,1] => 113
[12,5] => 107
[12,4,1] => 202
[12,3,2] => 209
[12,3,1,1] => 243
[12,2,2,1] => 219
[12,2,1,1,1] => 221
[12,1,1,1,1,1] => 127
[11,6] => 107
[11,5,1] => 215
[11,4,2] => 250
[11,4,1,1] => 281
[11,3,3] => 206
[11,3,2,1] => 329
[11,3,1,1,1] => 296
[11,2,2,2] => 218
[11,2,2,1,1] => 278
[11,2,1,1,1,1] => 251
[11,1,1,1,1,1,1] => 137
[10,7] => 101
[10,6,1] => 213
[10,5,2] => 267
[10,5,1,1] => 295
[10,4,3] => 257
[10,4,2,1] => 394
[10,4,1,1,1] => 338
[10,3,3,1] => 332
[10,3,2,2] => 334
[10,3,2,1,1] => 419
[10,3,1,1,1,1] => 333
[10,2,2,2,1] => 293
[10,2,2,1,1,1] => 321
[10,2,1,1,1,1,1] => 271
[10,1,1,1,1,1,1,1] => 143
[9,8] => 89
[9,7,1] => 196
[9,6,2] => 260
[9,6,1,1] => 285
[9,5,3] => 275
[9,5,2,1] => 414
[9,5,1,1,1] => 347
[9,4,4] => 235
[9,4,3,1] => 417
[9,4,2,2] => 396
[9,4,2,1,1] => 494
[9,4,1,1,1,1] => 373
[9,3,3,2] => 347
[9,3,3,1,1] => 422
[9,3,2,2,1] => 454
[9,3,2,1,1,1] => 479
[9,3,1,1,1,1,1] => 354
[9,2,2,2,2] => 275
[9,2,2,2,1,1] => 346
[9,2,2,1,1,1,1] => 348
[9,2,1,1,1,1,1,1] => 281
[9,1,1,1,1,1,1,1,1] => 145
[8,8,1] => 164
[8,7,2] => 229
[8,7,1,1] => 251
[8,6,3] => 260
[8,6,2,1] => 389
[8,6,1,1,1] => 323
[8,5,4] => 251
[8,5,3,1] => 436
[8,5,2,2] => 404
[8,5,2,1,1] => 503
[8,5,1,1,1,1] => 371
[8,4,4,1] => 378
[8,4,3,2] => 435
[8,4,3,1,1] => 519
[8,4,2,2,1] => 528
[8,4,2,1,1,1] => 550
[8,4,1,1,1,1,1] => 386
[8,3,3,3] => 310
[8,3,3,2,1] => 477
[8,3,3,1,1,1] => 476
[8,3,2,2,2] => 422
[8,3,2,2,1,1] => 530
[8,3,2,1,1,1,1] => 509
[8,3,1,1,1,1,1,1] => 359
[8,2,2,2,2,1] => 335
[8,2,2,2,1,1,1] => 377
[8,2,2,1,1,1,1,1] => 359
[8,2,1,1,1,1,1,1,1] => 281
[8,1,1,1,1,1,1,1,1,1] => 143
[7,7,3] => 212
[7,7,2,1] => 319
[7,7,1,1,1] => 266
[7,6,4] => 225
[7,6,3,1] => 389
[7,6,2,2] => 358
[7,6,2,1,1] => 446
[7,6,1,1,1,1] => 327
[7,5,5] => 207
[7,5,4,1] => 389
[7,5,3,2] => 436
[7,5,3,1,1] => 517
[7,5,2,2,1] => 515
[7,5,2,1,1,1] => 534
[7,5,1,1,1,1,1] => 367
[7,4,4,2] => 387
[7,4,4,1,1] => 457
[7,4,3,3] => 378
[7,4,3,2,1] => 582
[7,4,3,1,1,1] => 563
[7,4,2,2,2] => 473
[7,4,2,2,1,1] => 594
[7,4,2,1,1,1,1] => 562
[7,4,1,1,1,1,1,1] => 377
[7,3,3,3,1] => 423
[7,3,3,2,2] => 439
[7,3,3,2,1,1] => 549
[7,3,3,1,1,1,1] => 494
[7,3,2,2,2,1] => 507
[7,3,2,2,1,1,1] => 562
[7,3,2,1,1,1,1,1] => 509
[7,3,1,1,1,1,1,1,1] => 348
[7,2,2,2,2,2] => 297
[7,2,2,2,2,1,1] => 367
[7,2,2,2,1,1,1,1] => 386
[7,2,2,1,1,1,1,1,1] => 354
[7,2,1,1,1,1,1,1,1,1] => 271
[7,1,1,1,1,1,1,1,1,1,1] => 137
[6,6,5] => 167
[6,6,4,1] => 313
[6,6,3,2] => 350
[6,6,3,1,1] => 416
[6,6,2,2,1] => 415
[6,6,2,1,1,1] => 431
[6,6,1,1,1,1,1] => 297
[6,5,5,1] => 301
[6,5,4,2] => 370
[6,5,4,1,1] => 433
[6,5,3,3] => 350
[6,5,3,2,1] => 540
[6,5,3,1,1,1] => 518
[6,5,2,2,2] => 428
[6,5,2,2,1,1] => 538
[6,5,2,1,1,1,1] => 507
[6,5,1,1,1,1,1,1] => 335
[6,4,4,3] => 325
[6,4,4,2,1] => 496
[6,4,4,1,1,1] => 472
[6,4,3,3,1] => 493
[6,4,3,2,2] => 506
[6,4,3,2,1,1] => 631
[6,4,3,1,1,1,1] => 549
[6,4,2,2,2,1] => 538
[6,4,2,2,1,1,1] => 594
[6,4,2,1,1,1,1,1] => 530
[6,4,1,1,1,1,1,1,1] => 346
[6,3,3,3,2] => 383
[6,3,3,3,1,1] => 472
[6,3,3,2,2,1] => 518
[6,3,3,2,1,1,1] => 563
[6,3,3,1,1,1,1,1] => 476
[6,3,2,2,2,2] => 431
[6,3,2,2,2,1,1] => 534
[6,3,2,2,1,1,1,1] => 550
[6,3,2,1,1,1,1,1,1] => 479
[6,3,1,1,1,1,1,1,1,1] => 321
[6,2,2,2,2,2,1] => 327
[6,2,2,2,2,1,1,1] => 371
[6,2,2,2,1,1,1,1,1] => 373
[6,2,2,1,1,1,1,1,1,1] => 333
[6,2,1,1,1,1,1,1,1,1,1] => 251
[6,1,1,1,1,1,1,1,1,1,1,1] => 127
[5,5,5,2] => 250
[5,5,5,1,1] => 295
[5,5,4,3] => 265
[5,5,4,2,1] => 405
[5,5,4,1,1,1] => 383
[5,5,3,3,1] => 395
[5,5,3,2,2] => 405
[5,5,3,2,1,1] => 506
[5,5,3,1,1,1,1] => 439
[5,5,2,2,2,1] => 428
[5,5,2,2,1,1,1] => 473
[5,5,2,1,1,1,1,1] => 422
[5,5,1,1,1,1,1,1,1] => 275
[5,4,4,4] => 235
[5,4,4,3,1] => 392
[5,4,4,2,2] => 395
[5,4,4,2,1,1] => 493
[5,4,4,1,1,1,1] => 423
[5,4,3,3,2] => 405
[5,4,3,3,1,1] => 496
[5,4,3,2,2,1] => 540
[5,4,3,2,1,1,1] => 582
[5,4,3,1,1,1,1,1] => 477
[5,4,2,2,2,2] => 415
[5,4,2,2,2,1,1] => 515
[5,4,2,2,1,1,1,1] => 528
[5,4,2,1,1,1,1,1,1] => 454
[5,4,1,1,1,1,1,1,1,1] => 293
[5,3,3,3,3] => 295
[5,3,3,3,2,1] => 433
[5,3,3,3,1,1,1] => 457
[5,3,3,2,2,2] => 416
[5,3,3,2,2,1,1] => 517
[5,3,3,2,1,1,1,1] => 519
[5,3,3,1,1,1,1,1,1] => 422
[5,3,2,2,2,2,1] => 446
[5,3,2,2,2,1,1,1] => 503
[5,3,2,2,1,1,1,1,1] => 494
[5,3,2,1,1,1,1,1,1,1] => 419
[5,3,1,1,1,1,1,1,1,1,1] => 278
[5,2,2,2,2,2,2] => 266
[5,2,2,2,2,2,1,1] => 323
[5,2,2,2,2,1,1,1,1] => 347
[5,2,2,2,1,1,1,1,1,1] => 338
[5,2,2,1,1,1,1,1,1,1,1] => 296
[5,2,1,1,1,1,1,1,1,1,1,1] => 221
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 113
[4,4,4,4,1] => 235
[4,4,4,3,2] => 265
[4,4,4,3,1,1] => 325
[4,4,4,2,2,1] => 350
[4,4,4,2,1,1,1] => 378
[4,4,4,1,1,1,1,1] => 310
[4,4,3,3,3] => 250
[4,4,3,3,2,1] => 370
[4,4,3,3,1,1,1] => 387
[4,4,3,2,2,2] => 350
[4,4,3,2,2,1,1] => 436
[4,4,3,2,1,1,1,1] => 435
[4,4,3,1,1,1,1,1,1] => 347
[4,4,2,2,2,2,1] => 358
[4,4,2,2,2,1,1,1] => 404
[4,4,2,2,1,1,1,1,1] => 396
[4,4,2,1,1,1,1,1,1,1] => 334
[4,4,1,1,1,1,1,1,1,1,1] => 218
[4,3,3,3,3,1] => 301
[4,3,3,3,2,2] => 313
[4,3,3,3,2,1,1] => 389
[4,3,3,3,1,1,1,1] => 378
[4,3,3,2,2,2,1] => 389
[4,3,3,2,2,1,1,1] => 436
[4,3,3,2,1,1,1,1,1] => 417
[4,3,3,1,1,1,1,1,1,1] => 332
[4,3,2,2,2,2,2] => 319
[4,3,2,2,2,2,1,1] => 389
[4,3,2,2,2,1,1,1,1] => 414
[4,3,2,2,1,1,1,1,1,1] => 394
[4,3,2,1,1,1,1,1,1,1,1] => 329
[4,3,1,1,1,1,1,1,1,1,1,1] => 219
[4,2,2,2,2,2,2,1] => 251
[4,2,2,2,2,2,1,1,1] => 285
[4,2,2,2,2,1,1,1,1,1] => 295
[4,2,2,2,1,1,1,1,1,1,1] => 281
[4,2,2,1,1,1,1,1,1,1,1,1] => 243
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 181
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 95
[3,3,3,3,3,2] => 167
[3,3,3,3,3,1,1] => 207
[3,3,3,3,2,2,1] => 225
[3,3,3,3,2,1,1,1] => 251
[3,3,3,3,1,1,1,1,1] => 235
[3,3,3,2,2,2,2] => 212
[3,3,3,2,2,2,1,1] => 260
[3,3,3,2,2,1,1,1,1] => 275
[3,3,3,2,1,1,1,1,1,1] => 257
[3,3,3,1,1,1,1,1,1,1,1] => 206
[3,3,2,2,2,2,2,1] => 229
[3,3,2,2,2,2,1,1,1] => 260
[3,3,2,2,2,1,1,1,1,1] => 267
[3,3,2,2,1,1,1,1,1,1,1] => 250
[3,3,2,1,1,1,1,1,1,1,1,1] => 209
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 144
[3,2,2,2,2,2,2,2] => 164
[3,2,2,2,2,2,2,1,1] => 196
[3,2,2,2,2,2,1,1,1,1] => 213
[3,2,2,2,2,1,1,1,1,1,1] => 215
[3,2,2,2,1,1,1,1,1,1,1,1] => 202
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 174
-----------------------------------------------------------------------------
Created: Mar 03, 2019 at 21:56 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Mar 03, 2019 at 21:56 by Martin Rubey