*****************************************************************************
* 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: St001603
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The number of colourings of a polygon such that the multiplicities of a colour are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the dihedral 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 DihedralGroup(mu.size()).cycle_index().scalar(h(mu))
-----------------------------------------------------------------------------
Statistic values:
[3] => 1
[2,1] => 1
[1,1,1] => 1
[4] => 1
[3,1] => 1
[2,2] => 2
[2,1,1] => 2
[1,1,1,1] => 3
[5] => 1
[4,1] => 1
[3,2] => 2
[3,1,1] => 2
[2,2,1] => 4
[2,1,1,1] => 6
[1,1,1,1,1] => 12
[6] => 1
[5,1] => 1
[4,2] => 3
[4,1,1] => 3
[3,3] => 3
[3,2,1] => 6
[3,1,1,1] => 10
[2,2,2] => 11
[2,2,1,1] => 16
[2,1,1,1,1] => 30
[1,1,1,1,1,1] => 60
[7] => 1
[6,1] => 1
[5,2] => 3
[5,1,1] => 3
[4,3] => 4
[4,2,1] => 9
[4,1,1,1] => 15
[3,3,1] => 10
[3,2,2] => 18
[3,2,1,1] => 30
[3,1,1,1,1] => 60
[2,2,2,1] => 48
[2,2,1,1,1] => 90
[2,1,1,1,1,1] => 180
[1,1,1,1,1,1,1] => 360
[8] => 1
[7,1] => 1
[6,2] => 4
[6,1,1] => 4
[5,3] => 5
[5,2,1] => 12
[5,1,1,1] => 21
[4,4] => 8
[4,3,1] => 19
[4,2,2] => 33
[4,2,1,1] => 54
[4,1,1,1,1] => 105
[3,3,2] => 38
[3,3,1,1] => 70
[3,2,2,1] => 108
[3,2,1,1,1] => 210
[3,1,1,1,1,1] => 420
[2,2,2,2] => 171
[2,2,2,1,1] => 318
[2,2,1,1,1,1] => 630
[2,1,1,1,1,1,1] => 1260
[1,1,1,1,1,1,1,1] => 2520
[9] => 1
[8,1] => 1
[7,2] => 4
[7,1,1] => 4
[6,3] => 7
[6,2,1] => 16
[6,1,1,1] => 28
[5,4] => 10
[5,3,1] => 28
[5,2,2] => 48
[5,2,1,1] => 84
[5,1,1,1,1] => 168
[4,4,1] => 38
[4,3,2] => 76
[4,3,1,1] => 140
[4,2,2,1] => 216
[4,2,1,1,1] => 420
[4,1,1,1,1,1] => 840
[3,3,3] => 94
[3,3,2,1] => 280
[3,3,1,1,1] => 560
[3,2,2,2] => 432
[3,2,2,1,1] => 840
[3,2,1,1,1,1] => 1680
[3,1,1,1,1,1,1] => 3360
[2,2,2,2,1] => 1272
[2,2,2,1,1,1] => 2520
[2,2,1,1,1,1,1] => 5040
[2,1,1,1,1,1,1,1] => 10080
[1,1,1,1,1,1,1,1,1] => 20160
[10] => 1
[9,1] => 1
[8,2] => 5
[8,1,1] => 5
[7,3] => 8
[7,2,1] => 20
[7,1,1,1] => 36
[6,4] => 16
[6,3,1] => 44
[6,2,2] => 74
[6,2,1,1] => 128
[6,1,1,1,1] => 252
[5,5] => 16
[5,4,1] => 66
[5,3,2] => 132
[5,3,1,1] => 252
[5,2,2,1] => 384
[5,2,1,1,1] => 756
[5,1,1,1,1,1] => 1512
[4,4,2] => 174
[4,4,1,1] => 318
[4,3,3] => 216
[4,3,2,1] => 636
[4,3,1,1,1] => 1260
[4,2,2,2] => 978
[4,2,2,1,1] => 1896
[4,2,1,1,1,1] => 3780
[4,1,1,1,1,1,1] => 7560
[3,3,3,1] => 840
[3,3,2,2] => 1272
[3,3,2,1,1] => 2520
[3,3,1,1,1,1] => 5040
[3,2,2,2,1] => 3792
[3,2,2,1,1,1] => 7560
[3,2,1,1,1,1,1] => 15120
[3,1,1,1,1,1,1,1] => 30240
[2,2,2,2,2] => 5736
[2,2,2,2,1,1] => 11352
[2,2,2,1,1,1,1] => 22680
[2,2,1,1,1,1,1,1] => 45360
[2,1,1,1,1,1,1,1,1] => 90720
[1,1,1,1,1,1,1,1,1,1] => 181440
[11] => 1
[10,1] => 1
[9,2] => 5
[9,1,1] => 5
[8,3] => 10
[8,2,1] => 25
[8,1,1,1] => 45
[7,4] => 20
[7,3,1] => 60
[7,2,2] => 100
[7,2,1,1] => 180
[7,1,1,1,1] => 360
[6,5] => 26
[6,4,1] => 110
[6,3,2] => 220
[6,3,1,1] => 420
[6,2,2,1] => 640
[6,2,1,1,1] => 1260
[6,1,1,1,1,1] => 2520
[5,5,1] => 126
[5,4,2] => 330
[5,4,1,1] => 630
[5,3,3] => 420
[5,3,2,1] => 1260
[5,3,1,1,1] => 2520
[5,2,2,2] => 1920
[5,2,2,1,1] => 3780
[5,2,1,1,1,1] => 7560
[5,1,1,1,1,1,1] => 15120
[4,4,3] => 540
[4,4,2,1] => 1590
[4,4,1,1,1] => 3150
[4,3,3,1] => 2100
[4,3,2,2] => 3180
[4,3,2,1,1] => 6300
[4,3,1,1,1,1] => 12600
[4,2,2,2,1] => 9480
[4,2,2,1,1,1] => 18900
[4,2,1,1,1,1,1] => 37800
[4,1,1,1,1,1,1,1] => 75600
[3,3,3,2] => 4200
[3,3,3,1,1] => 8400
[3,3,2,2,1] => 12600
[3,3,2,1,1,1] => 25200
[3,3,1,1,1,1,1] => 50400
[3,2,2,2,2] => 18960
[3,2,2,2,1,1] => 37800
[3,2,2,1,1,1,1] => 75600
[3,2,1,1,1,1,1,1] => 151200
[3,1,1,1,1,1,1,1,1] => 302400
[2,2,2,2,2,1] => 56760
[2,2,2,2,1,1,1] => 113400
[2,2,2,1,1,1,1,1] => 226800
[2,2,1,1,1,1,1,1,1] => 453600
[2,1,1,1,1,1,1,1,1,1] => 907200
[1,1,1,1,1,1,1,1,1,1,1] => 1814400
[12] => 1
[11,1] => 1
[10,2] => 6
[10,1,1] => 6
[9,3] => 12
[9,2,1] => 30
[9,1,1,1] => 55
[8,4] => 29
[8,3,1] => 85
[8,2,2] => 140
[8,2,1,1] => 250
[8,1,1,1,1] => 495
[7,5] => 38
[7,4,1] => 170
[7,3,2] => 340
[7,3,1,1] => 660
[7,2,2,1] => 1000
[7,2,1,1,1] => 1980
[7,1,1,1,1,1] => 3960
[6,6] => 50
[6,5,1] => 236
[6,4,2] => 610
[6,4,1,1] => 1160
[6,3,3] => 781
[6,3,2,1] => 2320
[6,3,1,1,1] => 4620
[6,2,2,2] => 3530
[6,2,2,1,1] => 6940
[6,2,1,1,1,1] => 13860
[6,1,1,1,1,1,1] => 27720
[5,5,2] => 708
[5,5,1,1] => 1386
[5,4,3] => 1170
[5,4,2,1] => 3480
[5,4,1,1,1] => 6930
[5,3,3,1] => 4620
[5,3,2,2] => 6960
[5,3,2,1,1] => 13860
[5,3,1,1,1,1] => 27720
[5,2,2,2,1] => 20820
[5,2,2,1,1,1] => 41580
[5,2,1,1,1,1,1] => 83160
[5,1,1,1,1,1,1,1] => 166320
[4,4,4] => 1493
[4,4,3,1] => 5790
[4,4,2,2] => 8760
[4,4,2,1,1] => 17340
[4,4,1,1,1,1] => 34650
[4,3,3,2] => 11580
[4,3,3,1,1] => 23100
[4,3,2,2,1] => 34680
[4,3,2,1,1,1] => 69300
[4,3,1,1,1,1,1] => 138600
[4,2,2,2,2] => 52170
[4,2,2,2,1,1] => 103980
[4,2,2,1,1,1,1] => 207900
[4,2,1,1,1,1,1,1] => 415800
[4,1,1,1,1,1,1,1,1] => 831600
[3,3,3,3] => 15402
[3,3,3,2,1] => 46200
[3,3,3,1,1,1] => 92400
[3,3,2,2,2] => 69360
[3,3,2,2,1,1] => 138600
[3,3,2,1,1,1,1] => 277200
[3,3,1,1,1,1,1,1] => 554400
[3,2,2,2,2,1] => 207960
[3,2,2,2,1,1,1] => 415800
[3,2,2,1,1,1,1,1] => 831600
[3,2,1,1,1,1,1,1,1] => 1663200
[3,1,1,1,1,1,1,1,1,1] => 3326400
[2,2,2,2,2,2] => 312240
[2,2,2,2,2,1,1] => 623760
[2,2,2,2,1,1,1,1] => 1247400
[2,2,2,1,1,1,1,1,1] => 2494800
[2,2,1,1,1,1,1,1,1,1] => 4989600
[2,1,1,1,1,1,1,1,1,1,1] => 9979200
[1,1,1,1,1,1,1,1,1,1,1,1] => 19958400
[13] => 1
[12,1] => 1
[11,2] => 6
[11,1,1] => 6
[10,3] => 14
[10,2,1] => 36
[10,1,1,1] => 66
[9,4] => 35
[9,3,1] => 110
[9,2,2] => 180
[9,2,1,1] => 330
[9,1,1,1,1] => 660
[8,5] => 57
[8,4,1] => 255
[8,3,2] => 510
[8,3,1,1] => 990
[8,2,2,1] => 1500
[8,2,1,1,1] => 2970
[8,1,1,1,1,1] => 5940
[7,6] => 76
[7,5,1] => 396
[7,4,2] => 1020
[7,4,1,1] => 1980
[7,3,3] => 1320
[7,3,2,1] => 3960
[7,3,1,1,1] => 7920
[7,2,2,2] => 6000
[7,2,2,1,1] => 11880
[7,2,1,1,1,1] => 23760
[7,1,1,1,1,1,1] => 47520
[6,6,1] => 472
[6,5,2] => 1416
[6,5,1,1] => 2772
[6,4,3] => 2340
[6,4,2,1] => 6960
[6,4,1,1,1] => 13860
[6,3,3,1] => 9240
[6,3,2,2] => 13920
[6,3,2,1,1] => 27720
[6,3,1,1,1,1] => 55440
[6,2,2,2,1] => 41640
[6,2,2,1,1,1] => 83160
[6,2,1,1,1,1,1] => 166320
[6,1,1,1,1,1,1,1] => 332640
[5,5,3] => 2772
[5,5,2,1] => 8316
[5,5,1,1,1] => 16632
[5,4,4] => 3510
[5,4,3,1] => 13860
[5,4,2,2] => 20880
[5,4,2,1,1] => 41580
[5,4,1,1,1,1] => 83160
[5,3,3,2] => 27720
[5,3,3,1,1] => 55440
[5,3,2,2,1] => 83160
[5,3,2,1,1,1] => 166320
[5,3,1,1,1,1,1] => 332640
[5,2,2,2,2] => 124920
[5,2,2,2,1,1] => 249480
[5,2,2,1,1,1,1] => 498960
[5,2,1,1,1,1,1,1] => 997920
[5,1,1,1,1,1,1,1,1] => 1995840
[4,4,4,1] => 17370
[4,4,3,2] => 34740
[4,4,3,1,1] => 69300
[4,4,2,2,1] => 104040
[4,4,2,1,1,1] => 207900
[4,4,1,1,1,1,1] => 415800
[4,3,3,3] => 46200
[4,3,3,2,1] => 138600
[4,3,3,1,1,1] => 277200
[4,3,2,2,2] => 208080
[4,3,2,2,1,1] => 415800
[4,3,2,1,1,1,1] => 831600
[4,3,1,1,1,1,1,1] => 1663200
[4,2,2,2,2,1] => 623880
[4,2,2,2,1,1,1] => 1247400
[4,2,2,1,1,1,1,1] => 2494800
[4,2,1,1,1,1,1,1,1] => 4989600
[4,1,1,1,1,1,1,1,1,1] => 9979200
[3,3,3,3,1] => 184800
[3,3,3,2,2] => 277200
[3,3,3,2,1,1] => 554400
[3,3,3,1,1,1,1] => 1108800
[3,3,2,2,2,1] => 831600
[3,3,2,2,1,1,1] => 1663200
[3,3,2,1,1,1,1,1] => 3326400
[3,3,1,1,1,1,1,1,1] => 6652800
[3,2,2,2,2,2] => 1247760
[3,2,2,2,2,1,1] => 2494800
[3,2,2,2,1,1,1,1] => 4989600
[3,2,2,1,1,1,1,1,1] => 9979200
[3,2,1,1,1,1,1,1,1,1] => 19958400
[3,1,1,1,1,1,1,1,1,1,1] => 39916800
[2,2,2,2,2,2,1] => 3742560
[2,2,2,2,2,1,1,1] => 7484400
[2,2,2,2,1,1,1,1,1] => 14968800
[2,2,2,1,1,1,1,1,1,1] => 29937600
[2,2,1,1,1,1,1,1,1,1,1] => 59875200
[2,1,1,1,1,1,1,1,1,1,1,1] => 119750400
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 239500800
[14] => 1
[13,1] => 1
[12,2] => 7
[12,1,1] => 7
[11,3] => 16
[11,2,1] => 42
[11,1,1,1] => 78
[10,4] => 47
[10,3,1] => 146
[10,2,2] => 237
[10,2,1,1] => 432
[10,1,1,1,1] => 858
[9,5] => 79
[9,4,1] => 365
[9,3,2] => 730
[9,3,1,1] => 1430
[9,2,2,1] => 2160
[9,2,1,1,1] => 4290
[9,1,1,1,1,1] => 8580
[8,6] => 126
[8,5,1] => 651
[8,4,2] => 1665
[8,4,1,1] => 3225
[8,3,3] => 2160
[8,3,2,1] => 6450
[8,3,1,1,1] => 12870
[8,2,2,2] => 9765
[8,2,2,1,1] => 19320
[8,2,1,1,1,1] => 38610
[8,1,1,1,1,1,1] => 77220
[7,7] => 133
[7,6,1] => 868
[7,5,2] => 2604
[7,5,1,1] => 5148
[7,4,3] => 4320
[7,4,2,1] => 12900
[7,4,1,1,1] => 25740
[7,3,3,1] => 17160
[7,3,2,2] => 25800
[7,3,2,1,1] => 51480
[7,3,1,1,1,1] => 102960
[7,2,2,2,1] => 77280
[7,2,2,1,1,1] => 154440
[7,2,1,1,1,1,1] => 308880
[7,1,1,1,1,1,1,1] => 617760
[6,6,2] => 3078
[6,6,1,1] => 6016
[6,5,3] => 6036
[6,5,2,1] => 18048
[6,5,1,1,1] => 36036
[6,4,4] => 7620
[6,4,3,1] => 30060
[6,4,2,2] => 45270
[6,4,2,1,1] => 90120
[6,4,1,1,1,1] => 180180
[6,3,3,2] => 60120
[6,3,3,1,1] => 120120
[6,3,2,2,1] => 180240
[6,3,2,1,1,1] => 360360
[6,3,1,1,1,1,1] => 720720
[6,2,2,2,2] => 270720
[6,2,2,2,1,1] => 540600
[6,2,2,1,1,1,1] => 1081080
[6,2,1,1,1,1,1,1] => 2162160
[6,1,1,1,1,1,1,1,1] => 4324320
[5,5,4] => 9054
[5,5,3,1] => 36036
[5,5,2,2] => 54144
[5,5,2,1,1] => 108108
[5,5,1,1,1,1] => 216216
[5,4,4,1] => 45090
[5,4,3,2] => 90180
[5,4,3,1,1] => 180180
[5,4,2,2,1] => 270360
[5,4,2,1,1,1] => 540540
[5,4,1,1,1,1,1] => 1081080
[5,3,3,3] => 120120
[5,3,3,2,1] => 360360
[5,3,3,1,1,1] => 720720
[5,3,2,2,2] => 540720
[5,3,2,2,1,1] => 1081080
[5,3,2,1,1,1,1] => 2162160
[5,3,1,1,1,1,1,1] => 4324320
[5,2,2,2,2,1] => 1621800
[5,2,2,2,1,1,1] => 3243240
[5,2,2,1,1,1,1,1] => 6486480
[5,2,1,1,1,1,1,1,1] => 12972960
[5,1,1,1,1,1,1,1,1,1] => 25945920
[4,4,4,2] => 112950
[4,4,4,1,1] => 225270
[4,4,3,3] => 150240
[4,4,3,2,1] => 450540
[4,4,3,1,1,1] => 900900
[4,4,2,2,2] => 676350
[4,4,2,2,1,1] => 1351440
[4,4,2,1,1,1,1] => 2702700
[4,4,1,1,1,1,1,1] => 5405400
[4,3,3,3,1] => 600600
[4,3,3,2,2] => 901080
[4,3,3,2,1,1] => 1801800
[4,3,3,1,1,1,1] => 3603600
[4,3,2,2,2,1] => 2702880
[4,3,2,2,1,1,1] => 5405400
[4,3,2,1,1,1,1,1] => 10810800
[4,3,1,1,1,1,1,1,1] => 21621600
[4,2,2,2,2,2] => 4055400
[4,2,2,2,2,1,1] => 8108280
[4,2,2,2,1,1,1,1] => 16216200
[4,2,2,1,1,1,1,1,1] => 32432400
[4,2,1,1,1,1,1,1,1,1] => 64864800
[4,1,1,1,1,1,1,1,1,1,1] => 129729600
[3,3,3,3,2] => 1201200
[3,3,3,3,1,1] => 2402400
[3,3,3,2,2,1] => 3603600
[3,3,3,2,1,1,1] => 7207200
[3,3,3,1,1,1,1,1] => 14414400
[3,3,2,2,2,2] => 5405760
[3,3,2,2,2,1,1] => 10810800
[3,3,2,2,1,1,1,1] => 21621600
[3,3,2,1,1,1,1,1,1] => 43243200
[3,3,1,1,1,1,1,1,1,1] => 86486400
[3,2,2,2,2,2,1] => 16216560
[3,2,2,2,2,1,1,1] => 32432400
[3,2,2,2,1,1,1,1,1] => 64864800
[3,2,2,1,1,1,1,1,1,1] => 129729600
[3,2,1,1,1,1,1,1,1,1,1] => 259459200
[3,1,1,1,1,1,1,1,1,1,1,1] => 518918400
[2,2,2,2,2,2,2] => 24327000
[2,2,2,2,2,2,1,1] => 48648960
[2,2,2,2,2,1,1,1,1] => 97297200
[2,2,2,2,1,1,1,1,1,1] => 194594400
[2,2,2,1,1,1,1,1,1,1,1] => 389188800
[2,2,1,1,1,1,1,1,1,1,1,1] => 778377600
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 1556755200
[15] => 1
[14,1] => 1
[13,2] => 7
[13,1,1] => 7
[12,3] => 19
[12,2,1] => 49
[12,1,1,1] => 91
[11,4] => 56
[11,3,1] => 182
[11,2,2] => 294
[11,2,1,1] => 546
[11,1,1,1,1] => 1092
[10,5] => 111
[10,4,1] => 511
[10,3,2] => 1022
[10,3,1,1] => 2002
[10,2,2,1] => 3024
[10,2,1,1,1] => 6006
[10,1,1,1,1,1] => 12012
[9,6] => 185
[9,5,1] => 1001
[9,4,2] => 2555
[9,4,1,1] => 5005
[9,3,3] => 3338
[9,3,2,1] => 10010
[9,3,1,1,1] => 20020
[9,2,2,2] => 15120
[9,2,2,1,1] => 30030
[9,2,1,1,1,1] => 60060
[9,1,1,1,1,1,1] => 120120
[8,7] => 232
[8,6,1] => 1519
[8,5,2] => 4557
[8,5,1,1] => 9009
[8,4,3] => 7560
[8,4,2,1] => 22575
[8,4,1,1,1] => 45045
[8,3,3,1] => 30030
[8,3,2,2] => 45150
[8,3,2,1,1] => 90090
[8,3,1,1,1,1] => 180180
[8,2,2,2,1] => 135240
[8,2,2,1,1,1] => 270270
[8,2,1,1,1,1,1] => 540540
[8,1,1,1,1,1,1,1] => 1081080
[7,7,1] => 1716
[7,6,2] => 6076
[7,6,1,1] => 12012
[7,5,3] => 12012
[7,5,2,1] => 36036
[7,5,1,1,1] => 72072
[7,4,4] => 15120
[7,4,3,1] => 60060
[7,4,2,2] => 90300
[7,4,2,1,1] => 180180
[7,4,1,1,1,1] => 360360
[7,3,3,2] => 120120
[7,3,3,1,1] => 240240
[7,3,2,2,1] => 360360
[7,3,2,1,1,1] => 720720
[7,3,1,1,1,1,1] => 1441440
[7,2,2,2,2] => 540960
[7,2,2,2,1,1] => 1081080
[7,2,2,1,1,1,1] => 2162160
[7,2,1,1,1,1,1,1] => 4324320
[7,1,1,1,1,1,1,1,1] => 8648640
[6,6,3] => 14086
[6,6,2,1] => 42112
[6,6,1,1,1] => 84084
[6,5,4] => 21126
[6,5,3,1] => 84084
[6,5,2,2] => 126336
[6,5,2,1,1] => 252252
[6,5,1,1,1,1] => 504504
[6,4,4,1] => 105210
[6,4,3,2] => 210420
[6,4,3,1,1] => 420420
[6,4,2,2,1] => 630840
[6,4,2,1,1,1] => 1261260
[6,4,1,1,1,1,1] => 2522520
[6,3,3,3] => 280284
[6,3,3,2,1] => 840840
[6,3,3,1,1,1] => 1681680
[6,3,2,2,2] => 1261680
[6,3,2,2,1,1] => 2522520
[6,3,2,1,1,1,1] => 5045040
[6,3,1,1,1,1,1,1] => 10090080
[6,2,2,2,2,1] => 3784200
[6,2,2,2,1,1,1] => 7567560
[6,2,2,1,1,1,1,1] => 15135120
[6,2,1,1,1,1,1,1,1] => 30270240
[6,1,1,1,1,1,1,1,1,1] => 60540480
[5,5,5] => 25226
[5,5,4,1] => 126126
[5,5,3,2] => 252252
[5,5,3,1,1] => 504504
[5,5,2,2,1] => 756756
[5,5,2,1,1,1] => 1513512
[5,5,1,1,1,1,1] => 3027024
[5,4,4,2] => 315630
[5,4,4,1,1] => 630630
[5,4,3,3] => 420420
[5,4,3,2,1] => 1261260
[5,4,3,1,1,1] => 2522520
[5,4,2,2,2] => 1892520
[5,4,2,2,1,1] => 3783780
[5,4,2,1,1,1,1] => 7567560
[5,4,1,1,1,1,1,1] => 15135120
[5,3,3,3,1] => 1681680
[5,3,3,2,2] => 2522520
[5,3,3,2,1,1] => 5045040
[5,3,3,1,1,1,1] => 10090080
[5,3,2,2,2,1] => 7567560
[5,3,2,2,1,1,1] => 15135120
[5,3,2,1,1,1,1,1] => 30270240
[5,3,1,1,1,1,1,1,1] => 60540480
[5,2,2,2,2,2] => 11352600
[5,2,2,2,2,1,1] => 22702680
[5,2,2,2,1,1,1,1] => 45405360
[5,2,2,1,1,1,1,1,1] => 90810720
[5,2,1,1,1,1,1,1,1,1] => 181621440
[5,1,1,1,1,1,1,1,1,1,1] => 363242880
[4,4,4,3] => 525840
[4,4,4,2,1] => 1576890
[4,4,4,1,1,1] => 3153150
[4,4,3,3,1] => 2102100
[4,4,3,2,2] => 3153780
[4,4,3,2,1,1] => 6306300
[4,4,3,1,1,1,1] => 12612600
[4,4,2,2,2,1] => 9460080
[4,4,2,2,1,1,1] => 18918900
[4,4,2,1,1,1,1,1] => 37837800
[4,4,1,1,1,1,1,1,1] => 75675600
[4,3,3,3,2] => 4204200
[4,3,3,3,1,1] => 8408400
[4,3,3,2,2,1] => 12612600
[4,3,3,2,1,1,1] => 25225200
[4,3,3,1,1,1,1,1] => 50450400
[4,3,2,2,2,2] => 18920160
[4,3,2,2,2,1,1] => 37837800
[4,3,2,2,1,1,1,1] => 75675600
[4,3,2,1,1,1,1,1,1] => 151351200
[4,3,1,1,1,1,1,1,1,1] => 302702400
[4,2,2,2,2,2,1] => 56757960
[4,2,2,2,2,1,1,1] => 113513400
[4,2,2,2,1,1,1,1,1] => 227026800
[4,2,2,1,1,1,1,1,1,1] => 454053600
[4,2,1,1,1,1,1,1,1,1,1] => 908107200
[4,1,1,1,1,1,1,1,1,1,1,1] => 1816214400
[3,3,3,3,3] => 5605608
[3,3,3,3,2,1] => 16816800
[3,3,3,3,1,1,1] => 33633600
[3,3,3,2,2,2] => 25225200
[3,3,3,2,2,1,1] => 50450400
[3,3,3,2,1,1,1,1] => 100900800
[3,3,3,1,1,1,1,1,1] => 201801600
[3,3,2,2,2,2,1] => 75675600
[3,3,2,2,2,1,1,1] => 151351200
[3,3,2,2,1,1,1,1,1] => 302702400
[3,3,2,1,1,1,1,1,1,1] => 605404800
[3,3,1,1,1,1,1,1,1,1,1] => 1210809600
[3,2,2,2,2,2,2] => 113515920
[3,2,2,2,2,2,1,1] => 227026800
[3,2,2,2,2,1,1,1,1] => 454053600
[3,2,2,2,1,1,1,1,1,1] => 908107200
[3,2,2,1,1,1,1,1,1,1,1] => 1816214400
[2,2,2,2,2,2,2,1] => 340542720
[2,2,2,2,2,2,1,1,1] => 681080400
[2,2,2,2,2,1,1,1,1,1] => 1362160800
[16] => 1
[15,1] => 1
[14,2] => 8
[14,1,1] => 8
[13,3] => 21
[13,2,1] => 56
[13,1,1,1] => 105
[12,4] => 72
[12,3,1] => 231
[12,2,2] => 371
[12,2,1,1] => 686
[12,1,1,1,1] => 1365
[11,5] => 147
[11,4,1] => 693
[11,3,2] => 1386
[11,3,1,1] => 2730
[11,2,2,1] => 4116
[11,2,1,1,1] => 8190
[11,1,1,1,1,1] => 16380
[10,6] => 280
[10,5,1] => 1512
[10,4,2] => 3843
[10,4,1,1] => 7518
[10,3,3] => 5026
[10,3,2,1] => 15036
[10,3,1,1,1] => 30030
[10,2,2,2] => 22701
[10,2,2,1,1] => 45066
[10,2,1,1,1,1] => 90090
[10,1,1,1,1,1,1] => 180180
[9,7] => 375
[9,6,1] => 2520
[9,5,2] => 7560
[9,5,1,1] => 15015
[9,4,3] => 12565
[9,4,2,1] => 37590
[9,4,1,1,1] => 75075
[9,3,3,1] => 50050
[9,3,2,2] => 75180
[9,3,2,1,1] => 150150
[9,3,1,1,1,1] => 300300
[9,2,2,2,1] => 225330
[9,2,2,1,1,1] => 450450
[9,2,1,1,1,1,1] => 900900
[9,1,1,1,1,1,1,1] => 1801800
[8,8] => 440
[8,7,1] => 3235
[8,6,2] => 11410
[8,6,1,1] => 22540
[8,5,3] => 22575
[8,5,2,1] => 67620
[8,5,1,1,1] => 135135
[8,4,4] => 28377
[8,4,3,1] => 112665
[8,4,2,2] => 169365
[8,4,2,1,1] => 337890
[8,4,1,1,1,1] => 675675
[8,3,3,2] => 225330
[8,3,3,1,1] => 450450
[8,3,2,2,1] => 675780
[8,3,2,1,1,1] => 1351350
[8,3,1,1,1,1,1] => 2702700
[8,2,2,2,2] => 1014405
[8,2,2,2,1,1] => 2027130
[8,2,2,1,1,1,1] => 4054050
[8,2,1,1,1,1,1,1] => 8108100
[8,1,1,1,1,1,1,1,1] => 16216200
[7,7,2] => 12940
[7,7,1,1] => 25740
[7,6,3] => 30100
[7,6,2,1] => 90160
[7,6,1,1,1] => 180180
[7,5,4] => 45150
[7,5,3,1] => 180180
[7,5,2,2] => 270480
[7,5,2,1,1] => 540540
[7,5,1,1,1,1] => 1081080
[7,4,4,1] => 225330
[7,4,3,2] => 450660
[7,4,3,1,1] => 900900
[7,4,2,2,1] => 1351560
[7,4,2,1,1,1] => 2702700
[7,4,1,1,1,1,1] => 5405400
[7,3,3,3] => 600600
[7,3,3,2,1] => 1801800
[7,3,3,1,1,1] => 3603600
[7,3,2,2,2] => 2703120
[7,3,2,2,1,1] => 5405400
[7,3,2,1,1,1,1] => 10810800
[7,3,1,1,1,1,1,1] => 21621600
[7,2,2,2,2,1] => 8108520
[7,2,2,2,1,1,1] => 16216200
[7,2,2,1,1,1,1,1] => 32432400
[7,2,1,1,1,1,1,1,1] => 64864800
[7,1,1,1,1,1,1,1,1,1] => 129729600
[6,6,4] => 52850
[6,6,3,1] => 210280
[6,6,2,2] => 315910
[6,6,2,1,1] => 630700
[6,6,1,1,1,1] => 1261260
[6,5,5] => 63168
[6,5,4,1] => 315420
[6,5,3,2] => 630840
[6,5,3,1,1] => 1261260
[6,5,2,2,1] => 1892100
[6,5,2,1,1,1] => 3783780
[6,5,1,1,1,1,1] => 7567560
[6,4,4,2] => 789180
[6,4,4,1,1] => 1576680
[6,4,3,3] => 1051260
[6,4,3,2,1] => 3153360
[6,4,3,1,1,1] => 6306300
[6,4,2,2,2] => 4731510
[6,4,2,2,1,1] => 9459660
[6,4,2,1,1,1,1] => 18918900
[6,4,1,1,1,1,1,1] => 37837800
[6,3,3,3,1] => 4204200
[6,3,3,2,2] => 6306720
[6,3,3,2,1,1] => 12612600
[6,3,3,1,1,1,1] => 25225200
[6,3,2,2,2,1] => 18919320
[6,3,2,2,1,1,1] => 37837800
[6,3,2,1,1,1,1,1] => 75675600
[6,3,1,1,1,1,1,1,1] => 151351200
[6,2,2,2,2,2] => 28381920
[6,2,2,2,2,1,1] => 56757120
[6,2,2,2,1,1,1,1] => 113513400
[6,2,2,1,1,1,1,1,1] => 227026800
[6,2,1,1,1,1,1,1,1,1] => 454053600
[6,1,1,1,1,1,1,1,1,1,1] => 908107200
[5,5,5,1] => 378378
[5,5,4,2] => 946260
[5,5,4,1,1] => 1891890
[5,5,3,3] => 1261260
[5,5,3,2,1] => 3783780
[5,5,3,1,1,1] => 7567560
[5,5,2,2,2] => 5676300
[5,5,2,2,1,1] => 11351340
[5,5,2,1,1,1,1] => 22702680
[5,5,1,1,1,1,1,1] => 45405360
[5,4,4,3] => 1576890
[5,4,4,2,1] => 4730040
[5,4,4,1,1,1] => 9459450
[5,4,3,3,1] => 6306300
[5,4,3,2,2] => 9460080
[5,4,3,2,1,1] => 18918900
[5,4,3,1,1,1,1] => 37837800
[5,4,2,2,2,1] => 28378980
[5,4,2,2,1,1,1] => 56756700
[5,4,2,1,1,1,1,1] => 113513400
[5,4,1,1,1,1,1,1,1] => 227026800
[5,3,3,3,2] => 12612600
[5,3,3,3,1,1] => 25225200
[5,3,3,2,2,1] => 37837800
[5,3,3,2,1,1,1] => 75675600
[5,3,3,1,1,1,1,1] => 151351200
[5,3,2,2,2,2] => 56757960
[5,3,2,2,2,1,1] => 113513400
[5,3,2,2,1,1,1,1] => 227026800
[5,3,2,1,1,1,1,1,1] => 454053600
[5,3,1,1,1,1,1,1,1,1] => 908107200
[5,2,2,2,2,2,1] => 170271360
[5,2,2,2,2,1,1,1] => 340540200
[5,2,2,2,1,1,1,1,1] => 681080400
[5,2,2,1,1,1,1,1,1,1] => 1362160800
[4,4,4,4] => 1972059
[4,4,4,3,1] => 7883190
[4,4,4,2,2] => 11826990
[4,4,4,2,1,1] => 23648940
[4,4,4,1,1,1,1] => 47297250
[4,4,3,3,2] => 15766380
[4,4,3,3,1,1] => 31531500
[4,4,3,2,2,1] => 47297880
[4,4,3,2,1,1,1] => 94594500
[4,4,3,1,1,1,1,1] => 189189000
[4,4,2,2,2,2] => 70951230
[4,4,2,2,2,1,1] => 141892380
[4,4,2,2,1,1,1,1] => 283783500
[4,4,2,1,1,1,1,1,1] => 567567000
[4,4,1,1,1,1,1,1,1,1] => 1135134000
[4,3,3,3,3] => 21021000
[4,3,3,3,2,1] => 63063000
[4,3,3,3,1,1,1] => 126126000
[4,3,3,2,2,2] => 94595760
[4,3,3,2,2,1,1] => 189189000
[4,3,3,2,1,1,1,1] => 378378000
[4,3,3,1,1,1,1,1,1] => 756756000
[4,3,2,2,2,2,1] => 283784760
[4,3,2,2,2,1,1,1] => 567567000
[4,3,2,2,1,1,1,1,1] => 1135134000
[4,2,2,2,2,2,2] => 425685960
[4,2,2,2,2,2,1,1] => 851351760
[4,2,2,2,2,1,1,1,1] => 1702701000
[3,3,3,3,3,1] => 84084000
[3,3,3,3,2,2] => 126126000
[3,3,3,3,2,1,1] => 252252000
[3,3,3,3,1,1,1,1] => 504504000
[3,3,3,2,2,2,1] => 378378000
[3,3,3,2,2,1,1,1] => 756756000
[3,3,3,2,1,1,1,1,1] => 1513512000
[3,3,2,2,2,2,2] => 567569520
[3,3,2,2,2,2,1,1] => 1135134000
[3,2,2,2,2,2,2,1] => 1702703520
[17] => 1
[16,1] => 1
[15,2] => 8
[15,1,1] => 8
[14,3] => 24
[14,2,1] => 64
[14,1,1,1] => 120
[13,4] => 84
[13,3,1] => 280
[13,2,2] => 448
[13,2,1,1] => 840
[13,1,1,1,1] => 1680
[12,5] => 196
[12,4,1] => 924
[12,3,2] => 1848
[12,3,1,1] => 3640
[12,2,2,1] => 5488
[12,2,1,1,1] => 10920
[12,1,1,1,1,1] => 21840
[11,6] => 392
[11,5,1] => 2184
[11,4,2] => 5544
[11,4,1,1] => 10920
[11,3,3] => 7280
[11,3,2,1] => 21840
[11,3,1,1,1] => 43680
[11,2,2,2] => 32928
[11,2,2,1,1] => 65520
[11,2,1,1,1,1] => 131040
[11,1,1,1,1,1,1] => 262080
[10,7] => 600
[10,6,1] => 4032
[10,5,2] => 12096
[10,5,1,1] => 24024
[10,4,3] => 20104
[10,4,2,1] => 60144
[10,4,1,1,1] => 120120
[10,3,3,1] => 80080
[10,3,2,2] => 120288
[10,3,2,1,1] => 240240
[10,3,1,1,1,1] => 480480
[10,2,2,2,1] => 360528
[10,2,2,1,1,1] => 720720
[10,2,1,1,1,1,1] => 1441440
[10,1,1,1,1,1,1,1] => 2882880
[9,8] => 750
[9,7,1] => 5720
[9,6,2] => 20160
[9,6,1,1] => 40040
[9,5,3] => 40040
[9,5,2,1] => 120120
[9,5,1,1,1] => 240240
[9,4,4] => 50260
[9,4,3,1] => 200200
[9,4,2,2] => 300720
[9,4,2,1,1] => 600600
[9,4,1,1,1,1] => 1201200
[9,3,3,2] => 400400
[9,3,3,1,1] => 800800
[9,3,2,2,1] => 1201200
[9,3,2,1,1,1] => 2402400
[9,3,1,1,1,1,1] => 4804800
[9,2,2,2,2] => 1802640
[9,2,2,2,1,1] => 3603600
[9,2,2,1,1,1,1] => 7207200
[9,2,1,1,1,1,1,1] => 14414400
[9,1,1,1,1,1,1,1,1] => 28828800
[8,8,1] => 6470
[8,7,2] => 25880
[8,7,1,1] => 51480
[8,6,3] => 60200
[8,6,2,1] => 180320
[8,6,1,1,1] => 360360
[8,5,4] => 90300
[8,5,3,1] => 360360
[8,5,2,2] => 540960
[8,5,2,1,1] => 1081080
[8,5,1,1,1,1] => 2162160
[8,4,4,1] => 450660
[8,4,3,2] => 901320
[8,4,3,1,1] => 1801800
[8,4,2,2,1] => 2703120
[8,4,2,1,1,1] => 5405400
[8,4,1,1,1,1,1] => 10810800
[8,3,3,3] => 1201200
[8,3,3,2,1] => 3603600
[8,3,3,1,1,1] => 7207200
[8,3,2,2,2] => 5406240
[8,3,2,2,1,1] => 10810800
[8,3,2,1,1,1,1] => 21621600
[8,3,1,1,1,1,1,1] => 43243200
[8,2,2,2,2,1] => 16217040
[8,2,2,2,1,1,1] => 32432400
[8,2,2,1,1,1,1,1] => 64864800
[8,2,1,1,1,1,1,1,1] => 129729600
[8,1,1,1,1,1,1,1,1,1] => 259459200
[7,7,3] => 68640
[7,7,2,1] => 205920
[7,7,1,1,1] => 411840
[7,6,4] => 120400
[7,6,3,1] => 480480
[7,6,2,2] => 721280
[7,6,2,1,1] => 1441440
[7,6,1,1,1,1] => 2882880
[7,5,5] => 144144
[7,5,4,1] => 720720
[7,5,3,2] => 1441440
[7,5,3,1,1] => 2882880
[7,5,2,2,1] => 4324320
[7,5,2,1,1,1] => 8648640
[7,5,1,1,1,1,1] => 17297280
[7,4,4,2] => 1802640
[7,4,4,1,1] => 3603600
[7,4,3,3] => 2402400
[7,4,3,2,1] => 7207200
[7,4,3,1,1,1] => 14414400
[7,4,2,2,2] => 10812480
[7,4,2,2,1,1] => 21621600
[7,4,2,1,1,1,1] => 43243200
[7,4,1,1,1,1,1,1] => 86486400
[7,3,3,3,1] => 9609600
[7,3,3,2,2] => 14414400
[7,3,3,2,1,1] => 28828800
[7,3,3,1,1,1,1] => 57657600
[7,3,2,2,2,1] => 43243200
[7,3,2,2,1,1,1] => 86486400
[7,3,2,1,1,1,1,1] => 172972800
[7,3,1,1,1,1,1,1,1] => 345945600
[7,2,2,2,2,2] => 64868160
[7,2,2,2,2,1,1] => 129729600
[7,2,2,2,1,1,1,1] => 259459200
[7,2,2,1,1,1,1,1,1] => 518918400
[7,2,1,1,1,1,1,1,1,1] => 1037836800
[7,1,1,1,1,1,1,1,1,1,1] => 2075673600
[6,6,5] => 168448
[6,6,4,1] => 841120
[6,6,3,2] => 1682240
[6,6,3,1,1] => 3363360
[6,6,2,2,1] => 5045600
[6,6,2,1,1,1] => 10090080
[6,6,1,1,1,1,1] => 20180160
[6,5,5,1] => 1009008
[6,5,4,2] => 2523360
[6,5,4,1,1] => 5045040
[6,5,3,3] => 3363360
[6,5,3,2,1] => 10090080
[6,5,3,1,1,1] => 20180160
[6,5,2,2,2] => 15136800
[6,5,2,2,1,1] => 30270240
[6,5,2,1,1,1,1] => 60540480
[6,5,1,1,1,1,1,1] => 121080960
[6,4,4,3] => 4205040
[6,4,4,2,1] => 12613440
[6,4,4,1,1,1] => 25225200
[6,4,3,3,1] => 16816800
[6,4,3,2,2] => 25226880
[6,4,3,2,1,1] => 50450400
[6,4,3,1,1,1,1] => 100900800
[6,4,2,2,2,1] => 75677280
[6,4,2,2,1,1,1] => 151351200
[6,4,2,1,1,1,1,1] => 302702400
[6,4,1,1,1,1,1,1,1] => 605404800
[6,3,3,3,2] => 33633600
[6,3,3,3,1,1] => 67267200
[6,3,3,2,2,1] => 100900800
[6,3,3,2,1,1,1] => 201801600
[6,3,3,1,1,1,1,1] => 403603200
[6,3,2,2,2,2] => 151354560
[6,3,2,2,2,1,1] => 302702400
[6,3,2,2,1,1,1,1] => 605404800
[6,3,2,1,1,1,1,1,1] => 1210809600
[6,2,2,2,2,2,1] => 454056960
[6,2,2,2,2,1,1,1] => 908107200
[6,2,2,2,1,1,1,1,1] => 1816214400
[5,5,5,2] => 3027024
[5,5,5,1,1] => 6054048
[5,5,4,3] => 5045040
[5,5,4,2,1] => 15135120
[5,5,4,1,1,1] => 30270240
[5,5,3,3,1] => 20180160
[5,5,3,2,2] => 30270240
[5,5,3,2,1,1] => 60540480
[5,5,3,1,1,1,1] => 121080960
[5,5,2,2,2,1] => 90810720
[5,5,2,2,1,1,1] => 181621440
[5,5,2,1,1,1,1,1] => 363242880
[5,5,1,1,1,1,1,1,1] => 726485760
[5,4,4,4] => 6307560
[5,4,4,3,1] => 25225200
[5,4,4,2,2] => 37840320
[5,4,4,2,1,1] => 75675600
[5,4,4,1,1,1,1] => 151351200
[5,4,3,3,2] => 50450400
[5,4,3,3,1,1] => 100900800
[5,4,3,2,2,1] => 151351200
[5,4,3,2,1,1,1] => 302702400
[5,4,3,1,1,1,1,1] => 605404800
[5,4,2,2,2,2] => 227031840
[5,4,2,2,2,1,1] => 454053600
[5,4,2,2,1,1,1,1] => 908107200
[5,4,2,1,1,1,1,1,1] => 1816214400
[5,3,3,3,3] => 67267200
[5,3,3,3,2,1] => 201801600
[5,3,3,3,1,1,1] => 403603200
[5,3,3,2,2,2] => 302702400
[5,3,3,2,2,1,1] => 605404800
[5,3,3,2,1,1,1,1] => 1210809600
[5,3,2,2,2,2,1] => 908107200
[5,3,2,2,2,1,1,1] => 1816214400
[5,2,2,2,2,2,2] => 1362170880
[4,4,4,4,1] => 31532760
[4,4,4,3,2] => 63065520
[4,4,4,3,1,1] => 126126000
[4,4,4,2,2,1] => 189191520
[4,4,4,2,1,1,1] => 378378000
[4,4,4,1,1,1,1,1] => 756756000
[4,4,3,3,3] => 84084000
[4,4,3,3,2,1] => 252252000
[4,4,3,3,1,1,1] => 504504000
[4,4,3,2,2,2] => 378383040
[4,4,3,2,2,1,1] => 756756000
[4,4,3,2,1,1,1,1] => 1513512000
[4,4,2,2,2,2,1] => 1135139040
[4,3,3,3,3,1] => 336336000
[4,3,3,3,2,2] => 504504000
[4,3,3,3,2,1,1] => 1009008000
[4,3,3,3,1,1,1,1] => 2018016000
[4,3,3,2,2,2,1] => 1513512000
[3,3,3,3,3,2] => 672672000
[3,3,3,3,3,1,1] => 1345344000
[3,3,3,3,2,2,1] => 2018016000
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Created: Sep 27, 2020 at 11:53 by Martin Rubey
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Last Updated: Sep 27, 2020 at 11:53 by Martin Rubey