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* 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 *
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-----------------------------------------------------------------------------
Statistic identifier: St001605
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The number of colourings of a cycle such that the multiplicities of colours are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the cyclic group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(mu):
# h is the basis dual to m
h = SymmetricFunctions(QQ).h()
return CyclicPermutationGroup(mu.size()).cycle_index().scalar(h(mu))
-----------------------------------------------------------------------------
Statistic values:
[3] => 1
[2,1] => 1
[1,1,1] => 2
[4] => 1
[3,1] => 1
[2,2] => 2
[2,1,1] => 3
[1,1,1,1] => 6
[5] => 1
[4,1] => 1
[3,2] => 2
[3,1,1] => 4
[2,2,1] => 6
[2,1,1,1] => 12
[1,1,1,1,1] => 24
[6] => 1
[5,1] => 1
[4,2] => 3
[4,1,1] => 5
[3,3] => 4
[3,2,1] => 10
[3,1,1,1] => 20
[2,2,2] => 16
[2,2,1,1] => 30
[2,1,1,1,1] => 60
[1,1,1,1,1,1] => 120
[7] => 1
[6,1] => 1
[5,2] => 3
[5,1,1] => 6
[4,3] => 5
[4,2,1] => 15
[4,1,1,1] => 30
[3,3,1] => 20
[3,2,2] => 30
[3,2,1,1] => 60
[3,1,1,1,1] => 120
[2,2,2,1] => 90
[2,2,1,1,1] => 180
[2,1,1,1,1,1] => 360
[1,1,1,1,1,1,1] => 720
[8] => 1
[7,1] => 1
[6,2] => 4
[6,1,1] => 7
[5,3] => 7
[5,2,1] => 21
[5,1,1,1] => 42
[4,4] => 10
[4,3,1] => 35
[4,2,2] => 54
[4,2,1,1] => 105
[4,1,1,1,1] => 210
[3,3,2] => 70
[3,3,1,1] => 140
[3,2,2,1] => 210
[3,2,1,1,1] => 420
[3,1,1,1,1,1] => 840
[2,2,2,2] => 318
[2,2,2,1,1] => 630
[2,2,1,1,1,1] => 1260
[2,1,1,1,1,1,1] => 2520
[1,1,1,1,1,1,1,1] => 5040
[9] => 1
[8,1] => 1
[7,2] => 4
[7,1,1] => 8
[6,3] => 10
[6,2,1] => 28
[6,1,1,1] => 56
[5,4] => 14
[5,3,1] => 56
[5,2,2] => 84
[5,2,1,1] => 168
[5,1,1,1,1] => 336
[4,4,1] => 70
[4,3,2] => 140
[4,3,1,1] => 280
[4,2,2,1] => 420
[4,2,1,1,1] => 840
[4,1,1,1,1,1] => 1680
[3,3,3] => 188
[3,3,2,1] => 560
[3,3,1,1,1] => 1120
[3,2,2,2] => 840
[3,2,2,1,1] => 1680
[3,2,1,1,1,1] => 3360
[3,1,1,1,1,1,1] => 6720
[2,2,2,2,1] => 2520
[2,2,2,1,1,1] => 5040
[2,2,1,1,1,1,1] => 10080
[2,1,1,1,1,1,1,1] => 20160
[1,1,1,1,1,1,1,1,1] => 40320
[10] => 1
[9,1] => 1
[8,2] => 5
[8,1,1] => 9
[7,3] => 12
[7,2,1] => 36
[7,1,1,1] => 72
[6,4] => 22
[6,3,1] => 84
[6,2,2] => 128
[6,2,1,1] => 252
[6,1,1,1,1] => 504
[5,5] => 26
[5,4,1] => 126
[5,3,2] => 252
[5,3,1,1] => 504
[5,2,2,1] => 756
[5,2,1,1,1] => 1512
[5,1,1,1,1,1] => 3024
[4,4,2] => 318
[4,4,1,1] => 630
[4,3,3] => 420
[4,3,2,1] => 1260
[4,3,1,1,1] => 2520
[4,2,2,2] => 1896
[4,2,2,1,1] => 3780
[4,2,1,1,1,1] => 7560
[4,1,1,1,1,1,1] => 15120
[3,3,3,1] => 1680
[3,3,2,2] => 2520
[3,3,2,1,1] => 5040
[3,3,1,1,1,1] => 10080
[3,2,2,2,1] => 7560
[3,2,2,1,1,1] => 15120
[3,2,1,1,1,1,1] => 30240
[3,1,1,1,1,1,1,1] => 60480
[2,2,2,2,2] => 11352
[2,2,2,2,1,1] => 22680
[2,2,2,1,1,1,1] => 45360
[2,2,1,1,1,1,1,1] => 90720
[2,1,1,1,1,1,1,1,1] => 181440
[1,1,1,1,1,1,1,1,1,1] => 362880
[11] => 1
[10,1] => 1
[9,2] => 5
[9,1,1] => 10
[8,3] => 15
[8,2,1] => 45
[8,1,1,1] => 90
[7,4] => 30
[7,3,1] => 120
[7,2,2] => 180
[7,2,1,1] => 360
[7,1,1,1,1] => 720
[6,5] => 42
[6,4,1] => 210
[6,3,2] => 420
[6,3,1,1] => 840
[6,2,2,1] => 1260
[6,2,1,1,1] => 2520
[6,1,1,1,1,1] => 5040
[5,5,1] => 252
[5,4,2] => 630
[5,4,1,1] => 1260
[5,3,3] => 840
[5,3,2,1] => 2520
[5,3,1,1,1] => 5040
[5,2,2,2] => 3780
[5,2,2,1,1] => 7560
[5,2,1,1,1,1] => 15120
[5,1,1,1,1,1,1] => 30240
[4,4,3] => 1050
[4,4,2,1] => 3150
[4,4,1,1,1] => 6300
[4,3,3,1] => 4200
[4,3,2,2] => 6300
[4,3,2,1,1] => 12600
[4,3,1,1,1,1] => 25200
[4,2,2,2,1] => 18900
[4,2,2,1,1,1] => 37800
[4,2,1,1,1,1,1] => 75600
[4,1,1,1,1,1,1,1] => 151200
[3,3,3,2] => 8400
[3,3,3,1,1] => 16800
[3,3,2,2,1] => 25200
[3,3,2,1,1,1] => 50400
[3,3,1,1,1,1,1] => 100800
[3,2,2,2,2] => 37800
[3,2,2,2,1,1] => 75600
[3,2,2,1,1,1,1] => 151200
[3,2,1,1,1,1,1,1] => 302400
[3,1,1,1,1,1,1,1,1] => 604800
[2,2,2,2,2,1] => 113400
[2,2,2,2,1,1,1] => 226800
[2,2,2,1,1,1,1,1] => 453600
[2,2,1,1,1,1,1,1,1] => 907200
[2,1,1,1,1,1,1,1,1,1] => 1814400
[1,1,1,1,1,1,1,1,1,1,1] => 3628800
[12] => 1
[11,1] => 1
[10,2] => 6
[10,1,1] => 11
[9,3] => 19
[9,2,1] => 55
[9,1,1,1] => 110
[8,4] => 43
[8,3,1] => 165
[8,2,2] => 250
[8,2,1,1] => 495
[8,1,1,1,1] => 990
[7,5] => 66
[7,4,1] => 330
[7,3,2] => 660
[7,3,1,1] => 1320
[7,2,2,1] => 1980
[7,2,1,1,1] => 3960
[7,1,1,1,1,1] => 7920
[6,6] => 80
[6,5,1] => 462
[6,4,2] => 1160
[6,4,1,1] => 2310
[6,3,3] => 1542
[6,3,2,1] => 4620
[6,3,1,1,1] => 9240
[6,2,2,2] => 6940
[6,2,2,1,1] => 13860
[6,2,1,1,1,1] => 27720
[6,1,1,1,1,1,1] => 55440
[5,5,2] => 1386
[5,5,1,1] => 2772
[5,4,3] => 2310
[5,4,2,1] => 6930
[5,4,1,1,1] => 13860
[5,3,3,1] => 9240
[5,3,2,2] => 13860
[5,3,2,1,1] => 27720
[5,3,1,1,1,1] => 55440
[5,2,2,2,1] => 41580
[5,2,2,1,1,1] => 83160
[5,2,1,1,1,1,1] => 166320
[5,1,1,1,1,1,1,1] => 332640
[4,4,4] => 2896
[4,4,3,1] => 11550
[4,4,2,2] => 17340
[4,4,2,1,1] => 34650
[4,4,1,1,1,1] => 69300
[4,3,3,2] => 23100
[4,3,3,1,1] => 46200
[4,3,2,2,1] => 69300
[4,3,2,1,1,1] => 138600
[4,3,1,1,1,1,1] => 277200
[4,2,2,2,2] => 103980
[4,2,2,2,1,1] => 207900
[4,2,2,1,1,1,1] => 415800
[4,2,1,1,1,1,1,1] => 831600
[4,1,1,1,1,1,1,1,1] => 1663200
[3,3,3,3] => 30804
[3,3,3,2,1] => 92400
[3,3,3,1,1,1] => 184800
[3,3,2,2,2] => 138600
[3,3,2,2,1,1] => 277200
[3,3,2,1,1,1,1] => 554400
[3,3,1,1,1,1,1,1] => 1108800
[3,2,2,2,2,1] => 415800
[3,2,2,2,1,1,1] => 831600
[3,2,2,1,1,1,1,1] => 1663200
[3,2,1,1,1,1,1,1,1] => 3326400
[3,1,1,1,1,1,1,1,1,1] => 6652800
[2,2,2,2,2,2] => 623760
[2,2,2,2,2,1,1] => 1247400
[2,2,2,2,1,1,1,1] => 2494800
[2,2,2,1,1,1,1,1,1] => 4989600
[2,2,1,1,1,1,1,1,1,1] => 9979200
[2,1,1,1,1,1,1,1,1,1,1] => 19958400
[1,1,1,1,1,1,1,1,1,1,1,1] => 39916800
[13] => 1
[12,1] => 1
[11,2] => 6
[11,1,1] => 12
[10,3] => 22
[10,2,1] => 66
[10,1,1,1] => 132
[9,4] => 55
[9,3,1] => 220
[9,2,2] => 330
[9,2,1,1] => 660
[9,1,1,1,1] => 1320
[8,5] => 99
[8,4,1] => 495
[8,3,2] => 990
[8,3,1,1] => 1980
[8,2,2,1] => 2970
[8,2,1,1,1] => 5940
[8,1,1,1,1,1] => 11880
[7,6] => 132
[7,5,1] => 792
[7,4,2] => 1980
[7,4,1,1] => 3960
[7,3,3] => 2640
[7,3,2,1] => 7920
[7,3,1,1,1] => 15840
[7,2,2,2] => 11880
[7,2,2,1,1] => 23760
[7,2,1,1,1,1] => 47520
[7,1,1,1,1,1,1] => 95040
[6,6,1] => 924
[6,5,2] => 2772
[6,5,1,1] => 5544
[6,4,3] => 4620
[6,4,2,1] => 13860
[6,4,1,1,1] => 27720
[6,3,3,1] => 18480
[6,3,2,2] => 27720
[6,3,2,1,1] => 55440
[6,3,1,1,1,1] => 110880
[6,2,2,2,1] => 83160
[6,2,2,1,1,1] => 166320
[6,2,1,1,1,1,1] => 332640
[6,1,1,1,1,1,1,1] => 665280
[5,5,3] => 5544
[5,5,2,1] => 16632
[5,5,1,1,1] => 33264
[5,4,4] => 6930
[5,4,3,1] => 27720
[5,4,2,2] => 41580
[5,4,2,1,1] => 83160
[5,4,1,1,1,1] => 166320
[5,3,3,2] => 55440
[5,3,3,1,1] => 110880
[5,3,2,2,1] => 166320
[5,3,2,1,1,1] => 332640
[5,3,1,1,1,1,1] => 665280
[5,2,2,2,2] => 249480
[5,2,2,2,1,1] => 498960
[5,2,2,1,1,1,1] => 997920
[5,2,1,1,1,1,1,1] => 1995840
[5,1,1,1,1,1,1,1,1] => 3991680
[4,4,4,1] => 34650
[4,4,3,2] => 69300
[4,4,3,1,1] => 138600
[4,4,2,2,1] => 207900
[4,4,2,1,1,1] => 415800
[4,4,1,1,1,1,1] => 831600
[4,3,3,3] => 92400
[4,3,3,2,1] => 277200
[4,3,3,1,1,1] => 554400
[4,3,2,2,2] => 415800
[4,3,2,2,1,1] => 831600
[4,3,2,1,1,1,1] => 1663200
[4,3,1,1,1,1,1,1] => 3326400
[4,2,2,2,2,1] => 1247400
[4,2,2,2,1,1,1] => 2494800
[4,2,2,1,1,1,1,1] => 4989600
[4,2,1,1,1,1,1,1,1] => 9979200
[4,1,1,1,1,1,1,1,1,1] => 19958400
[3,3,3,3,1] => 369600
[3,3,3,2,2] => 554400
[3,3,3,2,1,1] => 1108800
[3,3,3,1,1,1,1] => 2217600
[3,3,2,2,2,1] => 1663200
[3,3,2,2,1,1,1] => 3326400
[3,3,2,1,1,1,1,1] => 6652800
[3,3,1,1,1,1,1,1,1] => 13305600
[3,2,2,2,2,2] => 2494800
[3,2,2,2,2,1,1] => 4989600
[3,2,2,2,1,1,1,1] => 9979200
[3,2,2,1,1,1,1,1,1] => 19958400
[3,2,1,1,1,1,1,1,1,1] => 39916800
[3,1,1,1,1,1,1,1,1,1,1] => 79833600
[2,2,2,2,2,2,1] => 7484400
[2,2,2,2,2,1,1,1] => 14968800
[2,2,2,2,1,1,1,1,1] => 29937600
[2,2,2,1,1,1,1,1,1,1] => 59875200
[2,2,1,1,1,1,1,1,1,1,1] => 119750400
[2,1,1,1,1,1,1,1,1,1,1,1] => 239500800
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 479001600
[14] => 1
[13,1] => 1
[12,2] => 7
[12,1,1] => 13
[11,3] => 26
[11,2,1] => 78
[11,1,1,1] => 156
[10,4] => 73
[10,3,1] => 286
[10,2,2] => 432
[10,2,1,1] => 858
[10,1,1,1,1] => 1716
[9,5] => 143
[9,4,1] => 715
[9,3,2] => 1430
[9,3,1,1] => 2860
[9,2,2,1] => 4290
[9,2,1,1,1] => 8580
[9,1,1,1,1,1] => 17160
[8,6] => 217
[8,5,1] => 1287
[8,4,2] => 3225
[8,4,1,1] => 6435
[8,3,3] => 4290
[8,3,2,1] => 12870
[8,3,1,1,1] => 25740
[8,2,2,2] => 19320
[8,2,2,1,1] => 38610
[8,2,1,1,1,1] => 77220
[8,1,1,1,1,1,1] => 154440
[7,7] => 246
[7,6,1] => 1716
[7,5,2] => 5148
[7,5,1,1] => 10296
[7,4,3] => 8580
[7,4,2,1] => 25740
[7,4,1,1,1] => 51480
[7,3,3,1] => 34320
[7,3,2,2] => 51480
[7,3,2,1,1] => 102960
[7,3,1,1,1,1] => 205920
[7,2,2,2,1] => 154440
[7,2,2,1,1,1] => 308880
[7,2,1,1,1,1,1] => 617760
[7,1,1,1,1,1,1,1] => 1235520
[6,6,2] => 6016
[6,6,1,1] => 12012
[6,5,3] => 12012
[6,5,2,1] => 36036
[6,5,1,1,1] => 72072
[6,4,4] => 15030
[6,4,3,1] => 60060
[6,4,2,2] => 90120
[6,4,2,1,1] => 180180
[6,4,1,1,1,1] => 360360
[6,3,3,2] => 120120
[6,3,3,1,1] => 240240
[6,3,2,2,1] => 360360
[6,3,2,1,1,1] => 720720
[6,3,1,1,1,1,1] => 1441440
[6,2,2,2,2] => 540600
[6,2,2,2,1,1] => 1081080
[6,2,2,1,1,1,1] => 2162160
[6,2,1,1,1,1,1,1] => 4324320
[6,1,1,1,1,1,1,1,1] => 8648640
[5,5,4] => 18018
[5,5,3,1] => 72072
[5,5,2,2] => 108108
[5,5,2,1,1] => 216216
[5,5,1,1,1,1] => 432432
[5,4,4,1] => 90090
[5,4,3,2] => 180180
[5,4,3,1,1] => 360360
[5,4,2,2,1] => 540540
[5,4,2,1,1,1] => 1081080
[5,4,1,1,1,1,1] => 2162160
[5,3,3,3] => 240240
[5,3,3,2,1] => 720720
[5,3,3,1,1,1] => 1441440
[5,3,2,2,2] => 1081080
[5,3,2,2,1,1] => 2162160
[5,3,2,1,1,1,1] => 4324320
[5,3,1,1,1,1,1,1] => 8648640
[5,2,2,2,2,1] => 3243240
[5,2,2,2,1,1,1] => 6486480
[5,2,2,1,1,1,1,1] => 12972960
[5,2,1,1,1,1,1,1,1] => 25945920
[5,1,1,1,1,1,1,1,1,1] => 51891840
[4,4,4,2] => 225270
[4,4,4,1,1] => 450450
[4,4,3,3] => 300300
[4,4,3,2,1] => 900900
[4,4,3,1,1,1] => 1801800
[4,4,2,2,2] => 1351440
[4,4,2,2,1,1] => 2702700
[4,4,2,1,1,1,1] => 5405400
[4,4,1,1,1,1,1,1] => 10810800
[4,3,3,3,1] => 1201200
[4,3,3,2,2] => 1801800
[4,3,3,2,1,1] => 3603600
[4,3,3,1,1,1,1] => 7207200
[4,3,2,2,2,1] => 5405400
[4,3,2,2,1,1,1] => 10810800
[4,3,2,1,1,1,1,1] => 21621600
[4,3,1,1,1,1,1,1,1] => 43243200
[4,2,2,2,2,2] => 8108280
[4,2,2,2,2,1,1] => 16216200
[4,2,2,2,1,1,1,1] => 32432400
[4,2,2,1,1,1,1,1,1] => 64864800
[4,2,1,1,1,1,1,1,1,1] => 129729600
[4,1,1,1,1,1,1,1,1,1,1] => 259459200
[3,3,3,3,2] => 2402400
[3,3,3,3,1,1] => 4804800
[3,3,3,2,2,1] => 7207200
[3,3,3,2,1,1,1] => 14414400
[3,3,3,1,1,1,1,1] => 28828800
[3,3,2,2,2,2] => 10810800
[3,3,2,2,2,1,1] => 21621600
[3,3,2,2,1,1,1,1] => 43243200
[3,3,2,1,1,1,1,1,1] => 86486400
[3,3,1,1,1,1,1,1,1,1] => 172972800
[3,2,2,2,2,2,1] => 32432400
[3,2,2,2,2,1,1,1] => 64864800
[3,2,2,2,1,1,1,1,1] => 129729600
[3,2,2,1,1,1,1,1,1,1] => 259459200
[3,2,1,1,1,1,1,1,1,1,1] => 518918400
[3,1,1,1,1,1,1,1,1,1,1,1] => 1037836800
[2,2,2,2,2,2,2] => 48648960
[2,2,2,2,2,2,1,1] => 97297200
[2,2,2,2,2,1,1,1,1] => 194594400
[2,2,2,2,1,1,1,1,1,1] => 389188800
[2,2,2,1,1,1,1,1,1,1,1] => 778377600
[2,2,1,1,1,1,1,1,1,1,1,1] => 1556755200
[15] => 1
[14,1] => 1
[13,2] => 7
[13,1,1] => 14
[12,3] => 31
[12,2,1] => 91
[12,1,1,1] => 182
[11,4] => 91
[11,3,1] => 364
[11,2,2] => 546
[11,2,1,1] => 1092
[11,1,1,1,1] => 2184
[10,5] => 201
[10,4,1] => 1001
[10,3,2] => 2002
[10,3,1,1] => 4004
[10,2,2,1] => 6006
[10,2,1,1,1] => 12012
[10,1,1,1,1,1] => 24024
[9,6] => 335
[9,5,1] => 2002
[9,4,2] => 5005
[9,4,1,1] => 10010
[9,3,3] => 6676
[9,3,2,1] => 20020
[9,3,1,1,1] => 40040
[9,2,2,2] => 30030
[9,2,2,1,1] => 60060
[9,2,1,1,1,1] => 120120
[9,1,1,1,1,1,1] => 240240
[8,7] => 429
[8,6,1] => 3003
[8,5,2] => 9009
[8,5,1,1] => 18018
[8,4,3] => 15015
[8,4,2,1] => 45045
[8,4,1,1,1] => 90090
[8,3,3,1] => 60060
[8,3,2,2] => 90090
[8,3,2,1,1] => 180180
[8,3,1,1,1,1] => 360360
[8,2,2,2,1] => 270270
[8,2,2,1,1,1] => 540540
[8,2,1,1,1,1,1] => 1081080
[8,1,1,1,1,1,1,1] => 2162160
[7,7,1] => 3432
[7,6,2] => 12012
[7,6,1,1] => 24024
[7,5,3] => 24024
[7,5,2,1] => 72072
[7,5,1,1,1] => 144144
[7,4,4] => 30030
[7,4,3,1] => 120120
[7,4,2,2] => 180180
[7,4,2,1,1] => 360360
[7,4,1,1,1,1] => 720720
[7,3,3,2] => 240240
[7,3,3,1,1] => 480480
[7,3,2,2,1] => 720720
[7,3,2,1,1,1] => 1441440
[7,3,1,1,1,1,1] => 2882880
[7,2,2,2,2] => 1081080
[7,2,2,2,1,1] => 2162160
[7,2,2,1,1,1,1] => 4324320
[7,2,1,1,1,1,1,1] => 8648640
[7,1,1,1,1,1,1,1,1] => 17297280
[6,6,3] => 28032
[6,6,2,1] => 84084
[6,6,1,1,1] => 168168
[6,5,4] => 42042
[6,5,3,1] => 168168
[6,5,2,2] => 252252
[6,5,2,1,1] => 504504
[6,5,1,1,1,1] => 1009008
[6,4,4,1] => 210210
[6,4,3,2] => 420420
[6,4,3,1,1] => 840840
[6,4,2,2,1] => 1261260
[6,4,2,1,1,1] => 2522520
[6,4,1,1,1,1,1] => 5045040
[6,3,3,3] => 560568
[6,3,3,2,1] => 1681680
[6,3,3,1,1,1] => 3363360
[6,3,2,2,2] => 2522520
[6,3,2,2,1,1] => 5045040
[6,3,2,1,1,1,1] => 10090080
[6,3,1,1,1,1,1,1] => 20180160
[6,2,2,2,2,1] => 7567560
[6,2,2,2,1,1,1] => 15135120
[6,2,2,1,1,1,1,1] => 30270240
[6,2,1,1,1,1,1,1,1] => 60540480
[6,1,1,1,1,1,1,1,1,1] => 121080960
[5,5,5] => 50452
[5,5,4,1] => 252252
[5,5,3,2] => 504504
[5,5,3,1,1] => 1009008
[5,5,2,2,1] => 1513512
[5,5,2,1,1,1] => 3027024
[5,5,1,1,1,1,1] => 6054048
[5,4,4,2] => 630630
[5,4,4,1,1] => 1261260
[5,4,3,3] => 840840
[5,4,3,2,1] => 2522520
[5,4,3,1,1,1] => 5045040
[5,4,2,2,2] => 3783780
[5,4,2,2,1,1] => 7567560
[5,4,2,1,1,1,1] => 15135120
[5,4,1,1,1,1,1,1] => 30270240
[5,3,3,3,1] => 3363360
[5,3,3,2,2] => 5045040
[5,3,3,2,1,1] => 10090080
[5,3,3,1,1,1,1] => 20180160
[5,3,2,2,2,1] => 15135120
[5,3,2,2,1,1,1] => 30270240
[5,3,2,1,1,1,1,1] => 60540480
[5,3,1,1,1,1,1,1,1] => 121080960
[5,2,2,2,2,2] => 22702680
[5,2,2,2,2,1,1] => 45405360
[5,2,2,2,1,1,1,1] => 90810720
[5,2,2,1,1,1,1,1,1] => 181621440
[5,2,1,1,1,1,1,1,1,1] => 363242880
[5,1,1,1,1,1,1,1,1,1,1] => 726485760
[4,4,4,3] => 1051050
[4,4,4,2,1] => 3153150
[4,4,4,1,1,1] => 6306300
[4,4,3,3,1] => 4204200
[4,4,3,2,2] => 6306300
[4,4,3,2,1,1] => 12612600
[4,4,3,1,1,1,1] => 25225200
[4,4,2,2,2,1] => 18918900
[4,4,2,2,1,1,1] => 37837800
[4,4,2,1,1,1,1,1] => 75675600
[4,4,1,1,1,1,1,1,1] => 151351200
[4,3,3,3,2] => 8408400
[4,3,3,3,1,1] => 16816800
[4,3,3,2,2,1] => 25225200
[4,3,3,2,1,1,1] => 50450400
[4,3,3,1,1,1,1,1] => 100900800
[4,3,2,2,2,2] => 37837800
[4,3,2,2,2,1,1] => 75675600
[4,3,2,2,1,1,1,1] => 151351200
[4,3,2,1,1,1,1,1,1] => 302702400
[4,3,1,1,1,1,1,1,1,1] => 605404800
[4,2,2,2,2,2,1] => 113513400
[4,2,2,2,2,1,1,1] => 227026800
[4,2,2,2,1,1,1,1,1] => 454053600
[4,2,2,1,1,1,1,1,1,1] => 908107200
[4,2,1,1,1,1,1,1,1,1,1] => 1816214400
[3,3,3,3,3] => 11211216
[3,3,3,3,2,1] => 33633600
[3,3,3,3,1,1,1] => 67267200
[3,3,3,2,2,2] => 50450400
[3,3,3,2,2,1,1] => 100900800
[3,3,3,2,1,1,1,1] => 201801600
[3,3,3,1,1,1,1,1,1] => 403603200
[3,3,2,2,2,2,1] => 151351200
[3,3,2,2,2,1,1,1] => 302702400
[3,3,2,2,1,1,1,1,1] => 605404800
[3,3,2,1,1,1,1,1,1,1] => 1210809600
[3,2,2,2,2,2,2] => 227026800
[3,2,2,2,2,2,1,1] => 454053600
[3,2,2,2,2,1,1,1,1] => 908107200
[3,2,2,2,1,1,1,1,1,1] => 1816214400
[2,2,2,2,2,2,2,1] => 681080400
[2,2,2,2,2,2,1,1,1] => 1362160800
[16] => 1
[15,1] => 1
[14,2] => 8
[14,1,1] => 15
[13,3] => 35
[13,2,1] => 105
[13,1,1,1] => 210
[12,4] => 116
[12,3,1] => 455
[12,2,2] => 686
[12,2,1,1] => 1365
[12,1,1,1,1] => 2730
[11,5] => 273
[11,4,1] => 1365
[11,3,2] => 2730
[11,3,1,1] => 5460
[11,2,2,1] => 8190
[11,2,1,1,1] => 16380
[11,1,1,1,1,1] => 32760
[10,6] => 504
[10,5,1] => 3003
[10,4,2] => 7518
[10,4,1,1] => 15015
[10,3,3] => 10010
[10,3,2,1] => 30030
[10,3,1,1,1] => 60060
[10,2,2,2] => 45066
[10,2,2,1,1] => 90090
[10,2,1,1,1,1] => 180180
[10,1,1,1,1,1,1] => 360360
[9,7] => 715
[9,6,1] => 5005
[9,5,2] => 15015
[9,5,1,1] => 30030
[9,4,3] => 25025
[9,4,2,1] => 75075
[9,4,1,1,1] => 150150
[9,3,3,1] => 100100
[9,3,2,2] => 150150
[9,3,2,1,1] => 300300
[9,3,1,1,1,1] => 600600
[9,2,2,2,1] => 450450
[9,2,2,1,1,1] => 900900
[9,2,1,1,1,1,1] => 1801800
[9,1,1,1,1,1,1,1] => 3603600
[8,8] => 810
[8,7,1] => 6435
[8,6,2] => 22540
[8,6,1,1] => 45045
[8,5,3] => 45045
[8,5,2,1] => 135135
[8,5,1,1,1] => 270270
[8,4,4] => 56334
[8,4,3,1] => 225225
[8,4,2,2] => 337890
[8,4,2,1,1] => 675675
[8,4,1,1,1,1] => 1351350
[8,3,3,2] => 450450
[8,3,3,1,1] => 900900
[8,3,2,2,1] => 1351350
[8,3,2,1,1,1] => 2702700
[8,3,1,1,1,1,1] => 5405400
[8,2,2,2,2] => 2027130
[8,2,2,2,1,1] => 4054050
[8,2,2,1,1,1,1] => 8108100
[8,2,1,1,1,1,1,1] => 16216200
[8,1,1,1,1,1,1,1,1] => 32432400
[7,7,2] => 25740
[7,7,1,1] => 51480
[7,6,3] => 60060
[7,6,2,1] => 180180
[7,6,1,1,1] => 360360
[7,5,4] => 90090
[7,5,3,1] => 360360
[7,5,2,2] => 540540
[7,5,2,1,1] => 1081080
[7,5,1,1,1,1] => 2162160
[7,4,4,1] => 450450
[7,4,3,2] => 900900
[7,4,3,1,1] => 1801800
[7,4,2,2,1] => 2702700
[7,4,2,1,1,1] => 5405400
[7,4,1,1,1,1,1] => 10810800
[7,3,3,3] => 1201200
[7,3,3,2,1] => 3603600
[7,3,3,1,1,1] => 7207200
[7,3,2,2,2] => 5405400
[7,3,2,2,1,1] => 10810800
[7,3,2,1,1,1,1] => 21621600
[7,3,1,1,1,1,1,1] => 43243200
[7,2,2,2,2,1] => 16216200
[7,2,2,2,1,1,1] => 32432400
[7,2,2,1,1,1,1,1] => 64864800
[7,2,1,1,1,1,1,1,1] => 129729600
[7,1,1,1,1,1,1,1,1,1] => 259459200
[6,6,4] => 105140
[6,6,3,1] => 420420
[6,6,2,2] => 630700
[6,6,2,1,1] => 1261260
[6,6,1,1,1,1] => 2522520
[6,5,5] => 126126
[6,5,4,1] => 630630
[6,5,3,2] => 1261260
[6,5,3,1,1] => 2522520
[6,5,2,2,1] => 3783780
[6,5,2,1,1,1] => 7567560
[6,5,1,1,1,1,1] => 15135120
[6,4,4,2] => 1576680
[6,4,4,1,1] => 3153150
[6,4,3,3] => 2102100
[6,4,3,2,1] => 6306300
[6,4,3,1,1,1] => 12612600
[6,4,2,2,2] => 9459660
[6,4,2,2,1,1] => 18918900
[6,4,2,1,1,1,1] => 37837800
[6,4,1,1,1,1,1,1] => 75675600
[6,3,3,3,1] => 8408400
[6,3,3,2,2] => 12612600
[6,3,3,2,1,1] => 25225200
[6,3,3,1,1,1,1] => 50450400
[6,3,2,2,2,1] => 37837800
[6,3,2,2,1,1,1] => 75675600
[6,3,2,1,1,1,1,1] => 151351200
[6,3,1,1,1,1,1,1,1] => 302702400
[6,2,2,2,2,2] => 56757120
[6,2,2,2,2,1,1] => 113513400
[6,2,2,2,1,1,1,1] => 227026800
[6,2,2,1,1,1,1,1,1] => 454053600
[6,2,1,1,1,1,1,1,1,1] => 908107200
[6,1,1,1,1,1,1,1,1,1,1] => 1816214400
[5,5,5,1] => 756756
[5,5,4,2] => 1891890
[5,5,4,1,1] => 3783780
[5,5,3,3] => 2522520
[5,5,3,2,1] => 7567560
[5,5,3,1,1,1] => 15135120
[5,5,2,2,2] => 11351340
[5,5,2,2,1,1] => 22702680
[5,5,2,1,1,1,1] => 45405360
[5,5,1,1,1,1,1,1] => 90810720
[5,4,4,3] => 3153150
[5,4,4,2,1] => 9459450
[5,4,4,1,1,1] => 18918900
[5,4,3,3,1] => 12612600
[5,4,3,2,2] => 18918900
[5,4,3,2,1,1] => 37837800
[5,4,3,1,1,1,1] => 75675600
[5,4,2,2,2,1] => 56756700
[5,4,2,2,1,1,1] => 113513400
[5,4,2,1,1,1,1,1] => 227026800
[5,4,1,1,1,1,1,1,1] => 454053600
[5,3,3,3,2] => 25225200
[5,3,3,3,1,1] => 50450400
[5,3,3,2,2,1] => 75675600
[5,3,3,2,1,1,1] => 151351200
[5,3,3,1,1,1,1,1] => 302702400
[5,3,2,2,2,2] => 113513400
[5,3,2,2,2,1,1] => 227026800
[5,3,2,2,1,1,1,1] => 454053600
[5,3,2,1,1,1,1,1,1] => 908107200
[5,3,1,1,1,1,1,1,1,1] => 1816214400
[5,2,2,2,2,2,1] => 340540200
[5,2,2,2,2,1,1,1] => 681080400
[5,2,2,2,1,1,1,1,1] => 1362160800
[4,4,4,4] => 3941598
[4,4,4,3,1] => 15765750
[4,4,4,2,2] => 23648940
[4,4,4,2,1,1] => 47297250
[4,4,4,1,1,1,1] => 94594500
[4,4,3,3,2] => 31531500
[4,4,3,3,1,1] => 63063000
[4,4,3,2,2,1] => 94594500
[4,4,3,2,1,1,1] => 189189000
[4,4,3,1,1,1,1,1] => 378378000
[4,4,2,2,2,2] => 141892380
[4,4,2,2,2,1,1] => 283783500
[4,4,2,2,1,1,1,1] => 567567000
[4,4,2,1,1,1,1,1,1] => 1135134000
[4,3,3,3,3] => 42042000
[4,3,3,3,2,1] => 126126000
[4,3,3,3,1,1,1] => 252252000
[4,3,3,2,2,2] => 189189000
[4,3,3,2,2,1,1] => 378378000
[4,3,3,2,1,1,1,1] => 756756000
[4,3,3,1,1,1,1,1,1] => 1513512000
[4,3,2,2,2,2,1] => 567567000
[4,3,2,2,2,1,1,1] => 1135134000
[4,2,2,2,2,2,2] => 851351760
[4,2,2,2,2,2,1,1] => 1702701000
[3,3,3,3,3,1] => 168168000
[3,3,3,3,2,2] => 252252000
[3,3,3,3,2,1,1] => 504504000
[3,3,3,3,1,1,1,1] => 1009008000
[3,3,3,2,2,2,1] => 756756000
[3,3,3,2,2,1,1,1] => 1513512000
[3,3,2,2,2,2,2] => 1135134000
[17] => 1
[16,1] => 1
[15,2] => 8
[15,1,1] => 16
[14,3] => 40
[14,2,1] => 120
[14,1,1,1] => 240
[13,4] => 140
[13,3,1] => 560
[13,2,2] => 840
[13,2,1,1] => 1680
[13,1,1,1,1] => 3360
[12,5] => 364
[12,4,1] => 1820
[12,3,2] => 3640
[12,3,1,1] => 7280
[12,2,2,1] => 10920
[12,2,1,1,1] => 21840
[12,1,1,1,1,1] => 43680
[11,6] => 728
[11,5,1] => 4368
[11,4,2] => 10920
[11,4,1,1] => 21840
[11,3,3] => 14560
[11,3,2,1] => 43680
[11,3,1,1,1] => 87360
[11,2,2,2] => 65520
[11,2,2,1,1] => 131040
[11,2,1,1,1,1] => 262080
[11,1,1,1,1,1,1] => 524160
[10,7] => 1144
[10,6,1] => 8008
[10,5,2] => 24024
[10,5,1,1] => 48048
[10,4,3] => 40040
[10,4,2,1] => 120120
[10,4,1,1,1] => 240240
[10,3,3,1] => 160160
[10,3,2,2] => 240240
[10,3,2,1,1] => 480480
[10,3,1,1,1,1] => 960960
[10,2,2,2,1] => 720720
[10,2,2,1,1,1] => 1441440
[10,2,1,1,1,1,1] => 2882880
[10,1,1,1,1,1,1,1] => 5765760
[9,8] => 1430
[9,7,1] => 11440
[9,6,2] => 40040
[9,6,1,1] => 80080
[9,5,3] => 80080
[9,5,2,1] => 240240
[9,5,1,1,1] => 480480
[9,4,4] => 100100
[9,4,3,1] => 400400
[9,4,2,2] => 600600
[9,4,2,1,1] => 1201200
[9,4,1,1,1,1] => 2402400
[9,3,3,2] => 800800
[9,3,3,1,1] => 1601600
[9,3,2,2,1] => 2402400
[9,3,2,1,1,1] => 4804800
[9,3,1,1,1,1,1] => 9609600
[9,2,2,2,2] => 3603600
[9,2,2,2,1,1] => 7207200
[9,2,2,1,1,1,1] => 14414400
[9,2,1,1,1,1,1,1] => 28828800
[9,1,1,1,1,1,1,1,1] => 57657600
[8,8,1] => 12870
[8,7,2] => 51480
[8,7,1,1] => 102960
[8,6,3] => 120120
[8,6,2,1] => 360360
[8,6,1,1,1] => 720720
[8,5,4] => 180180
[8,5,3,1] => 720720
[8,5,2,2] => 1081080
[8,5,2,1,1] => 2162160
[8,5,1,1,1,1] => 4324320
[8,4,4,1] => 900900
[8,4,3,2] => 1801800
[8,4,3,1,1] => 3603600
[8,4,2,2,1] => 5405400
[8,4,2,1,1,1] => 10810800
[8,4,1,1,1,1,1] => 21621600
[8,3,3,3] => 2402400
[8,3,3,2,1] => 7207200
[8,3,3,1,1,1] => 14414400
[8,3,2,2,2] => 10810800
[8,3,2,2,1,1] => 21621600
[8,3,2,1,1,1,1] => 43243200
[8,3,1,1,1,1,1,1] => 86486400
[8,2,2,2,2,1] => 32432400
[8,2,2,2,1,1,1] => 64864800
[8,2,2,1,1,1,1,1] => 129729600
[8,2,1,1,1,1,1,1,1] => 259459200
[8,1,1,1,1,1,1,1,1,1] => 518918400
[7,7,3] => 137280
[7,7,2,1] => 411840
[7,7,1,1,1] => 823680
[7,6,4] => 240240
[7,6,3,1] => 960960
[7,6,2,2] => 1441440
[7,6,2,1,1] => 2882880
[7,6,1,1,1,1] => 5765760
[7,5,5] => 288288
[7,5,4,1] => 1441440
[7,5,3,2] => 2882880
[7,5,3,1,1] => 5765760
[7,5,2,2,1] => 8648640
[7,5,2,1,1,1] => 17297280
[7,5,1,1,1,1,1] => 34594560
[7,4,4,2] => 3603600
[7,4,4,1,1] => 7207200
[7,4,3,3] => 4804800
[7,4,3,2,1] => 14414400
[7,4,3,1,1,1] => 28828800
[7,4,2,2,2] => 21621600
[7,4,2,2,1,1] => 43243200
[7,4,2,1,1,1,1] => 86486400
[7,4,1,1,1,1,1,1] => 172972800
[7,3,3,3,1] => 19219200
[7,3,3,2,2] => 28828800
[7,3,3,2,1,1] => 57657600
[7,3,3,1,1,1,1] => 115315200
[7,3,2,2,2,1] => 86486400
[7,3,2,2,1,1,1] => 172972800
[7,3,2,1,1,1,1,1] => 345945600
[7,3,1,1,1,1,1,1,1] => 691891200
[7,2,2,2,2,2] => 129729600
[7,2,2,2,2,1,1] => 259459200
[7,2,2,2,1,1,1,1] => 518918400
[7,2,2,1,1,1,1,1,1] => 1037836800
[7,2,1,1,1,1,1,1,1,1] => 2075673600
[6,6,5] => 336336
[6,6,4,1] => 1681680
[6,6,3,2] => 3363360
[6,6,3,1,1] => 6726720
[6,6,2,2,1] => 10090080
[6,6,2,1,1,1] => 20180160
[6,6,1,1,1,1,1] => 40360320
[6,5,5,1] => 2018016
[6,5,4,2] => 5045040
[6,5,4,1,1] => 10090080
[6,5,3,3] => 6726720
[6,5,3,2,1] => 20180160
[6,5,3,1,1,1] => 40360320
[6,5,2,2,2] => 30270240
[6,5,2,2,1,1] => 60540480
[6,5,2,1,1,1,1] => 121080960
[6,5,1,1,1,1,1,1] => 242161920
[6,4,4,3] => 8408400
[6,4,4,2,1] => 25225200
[6,4,4,1,1,1] => 50450400
[6,4,3,3,1] => 33633600
[6,4,3,2,2] => 50450400
[6,4,3,2,1,1] => 100900800
[6,4,3,1,1,1,1] => 201801600
[6,4,2,2,2,1] => 151351200
[6,4,2,2,1,1,1] => 302702400
[6,4,2,1,1,1,1,1] => 605404800
[6,4,1,1,1,1,1,1,1] => 1210809600
[6,3,3,3,2] => 67267200
[6,3,3,3,1,1] => 134534400
[6,3,3,2,2,1] => 201801600
[6,3,3,2,1,1,1] => 403603200
[6,3,3,1,1,1,1,1] => 807206400
[6,3,2,2,2,2] => 302702400
[6,3,2,2,2,1,1] => 605404800
[6,3,2,2,1,1,1,1] => 1210809600
[6,2,2,2,2,2,1] => 908107200
[6,2,2,2,2,1,1,1] => 1816214400
[5,5,5,2] => 6054048
[5,5,5,1,1] => 12108096
[5,5,4,3] => 10090080
[5,5,4,2,1] => 30270240
[5,5,4,1,1,1] => 60540480
[5,5,3,3,1] => 40360320
[5,5,3,2,2] => 60540480
[5,5,3,2,1,1] => 121080960
[5,5,3,1,1,1,1] => 242161920
[5,5,2,2,2,1] => 181621440
[5,5,2,2,1,1,1] => 363242880
[5,5,2,1,1,1,1,1] => 726485760
[5,5,1,1,1,1,1,1,1] => 1452971520
[5,4,4,4] => 12612600
[5,4,4,3,1] => 50450400
[5,4,4,2,2] => 75675600
[5,4,4,2,1,1] => 151351200
[5,4,4,1,1,1,1] => 302702400
[5,4,3,3,2] => 100900800
[5,4,3,3,1,1] => 201801600
[5,4,3,2,2,1] => 302702400
[5,4,3,2,1,1,1] => 605404800
[5,4,3,1,1,1,1,1] => 1210809600
[5,4,2,2,2,2] => 454053600
[5,4,2,2,2,1,1] => 908107200
[5,4,2,2,1,1,1,1] => 1816214400
[5,3,3,3,3] => 134534400
[5,3,3,3,2,1] => 403603200
[5,3,3,3,1,1,1] => 807206400
[5,3,3,2,2,2] => 605404800
[5,3,3,2,2,1,1] => 1210809600
[5,3,2,2,2,2,1] => 1816214400
[4,4,4,4,1] => 63063000
[4,4,4,3,2] => 126126000
[4,4,4,3,1,1] => 252252000
[4,4,4,2,2,1] => 378378000
[4,4,4,2,1,1,1] => 756756000
[4,4,4,1,1,1,1,1] => 1513512000
[4,4,3,3,3] => 168168000
[4,4,3,3,2,1] => 504504000
[4,4,3,3,1,1,1] => 1009008000
[4,4,3,2,2,2] => 756756000
[4,4,3,2,2,1,1] => 1513512000
[4,3,3,3,3,1] => 672672000
[4,3,3,3,2,2] => 1009008000
[4,3,3,3,2,1,1] => 2018016000
[3,3,3,3,3,2] => 1345344000
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Created: Sep 27, 2020 at 11:57 by Martin Rubey
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Last Updated: Sep 27, 2020 at 11:57 by Martin Rubey