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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, *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St001378
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The product of the cohook lengths of the integer partition.
For a cell $c = (i,j)$, the '''cohook length''' of $c$ is $h^*(c) = i+j-1$. This statistic is then
$$\prod_{c \in \lambda} h^*(c).$$
-----------------------------------------------------------------------------
References: [1] Pak, I., Petrov, F., Sokolov, V. Hook inequalities [[arXiv:1903.11828]]
-----------------------------------------------------------------------------
Code:
def statistic(L):
return prod( sum(x)+1 for x in L.cells() )
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 2
[1,1] => 2
[3] => 6
[2,1] => 4
[1,1,1] => 6
[4] => 24
[3,1] => 12
[2,2] => 12
[2,1,1] => 12
[1,1,1,1] => 24
[5] => 120
[4,1] => 48
[3,2] => 36
[3,1,1] => 36
[2,2,1] => 36
[2,1,1,1] => 48
[1,1,1,1,1] => 120
[6] => 720
[5,1] => 240
[4,2] => 144
[4,1,1] => 144
[3,3] => 144
[3,2,1] => 108
[3,1,1,1] => 144
[2,2,2] => 144
[2,2,1,1] => 144
[2,1,1,1,1] => 240
[1,1,1,1,1,1] => 720
[7] => 5040
[6,1] => 1440
[5,2] => 720
[5,1,1] => 720
[4,3] => 576
[4,2,1] => 432
[4,1,1,1] => 576
[3,3,1] => 432
[3,2,2] => 432
[3,2,1,1] => 432
[3,1,1,1,1] => 720
[2,2,2,1] => 576
[2,2,1,1,1] => 720
[2,1,1,1,1,1] => 1440
[1,1,1,1,1,1,1] => 5040
[8] => 40320
[7,1] => 10080
[6,2] => 4320
[6,1,1] => 4320
[5,3] => 2880
[5,2,1] => 2160
[5,1,1,1] => 2880
[4,4] => 2880
[4,3,1] => 1728
[4,2,2] => 1728
[4,2,1,1] => 1728
[4,1,1,1,1] => 2880
[3,3,2] => 1728
[3,3,1,1] => 1728
[3,2,2,1] => 1728
[3,2,1,1,1] => 2160
[3,1,1,1,1,1] => 4320
[2,2,2,2] => 2880
[2,2,2,1,1] => 2880
[2,2,1,1,1,1] => 4320
[2,1,1,1,1,1,1] => 10080
[1,1,1,1,1,1,1,1] => 40320
[9] => 362880
[8,1] => 80640
[7,2] => 30240
[7,1,1] => 30240
[6,3] => 17280
[6,2,1] => 12960
[6,1,1,1] => 17280
[5,4] => 14400
[5,3,1] => 8640
[5,2,2] => 8640
[5,2,1,1] => 8640
[5,1,1,1,1] => 14400
[4,4,1] => 8640
[4,3,2] => 6912
[4,3,1,1] => 6912
[4,2,2,1] => 6912
[4,2,1,1,1] => 8640
[4,1,1,1,1,1] => 17280
[3,3,3] => 8640
[3,3,2,1] => 6912
[3,3,1,1,1] => 8640
[3,2,2,2] => 8640
[3,2,2,1,1] => 8640
[3,2,1,1,1,1] => 12960
[3,1,1,1,1,1,1] => 30240
[2,2,2,2,1] => 14400
[2,2,2,1,1,1] => 17280
[2,2,1,1,1,1,1] => 30240
[2,1,1,1,1,1,1,1] => 80640
[1,1,1,1,1,1,1,1,1] => 362880
[10] => 3628800
[9,1] => 725760
[8,2] => 241920
[8,1,1] => 241920
[7,3] => 120960
[7,2,1] => 90720
[7,1,1,1] => 120960
[6,4] => 86400
[6,3,1] => 51840
[6,2,2] => 51840
[6,2,1,1] => 51840
[6,1,1,1,1] => 86400
[5,5] => 86400
[5,4,1] => 43200
[5,3,2] => 34560
[5,3,1,1] => 34560
[5,2,2,1] => 34560
[5,2,1,1,1] => 43200
[5,1,1,1,1,1] => 86400
[4,4,2] => 34560
[4,4,1,1] => 34560
[4,3,3] => 34560
[4,3,2,1] => 27648
[4,3,1,1,1] => 34560
[4,2,2,2] => 34560
[4,2,2,1,1] => 34560
[4,2,1,1,1,1] => 51840
[4,1,1,1,1,1,1] => 120960
[3,3,3,1] => 34560
[3,3,2,2] => 34560
[3,3,2,1,1] => 34560
[3,3,1,1,1,1] => 51840
[3,2,2,2,1] => 43200
[3,2,2,1,1,1] => 51840
[3,2,1,1,1,1,1] => 90720
[3,1,1,1,1,1,1,1] => 241920
[2,2,2,2,2] => 86400
[2,2,2,2,1,1] => 86400
[2,2,2,1,1,1,1] => 120960
[2,2,1,1,1,1,1,1] => 241920
[2,1,1,1,1,1,1,1,1] => 725760
[1,1,1,1,1,1,1,1,1,1] => 3628800
[11] => 39916800
[10,1] => 7257600
[9,2] => 2177280
[9,1,1] => 2177280
[8,3] => 967680
[8,2,1] => 725760
[8,1,1,1] => 967680
[7,4] => 604800
[7,3,1] => 362880
[7,2,2] => 362880
[7,2,1,1] => 362880
[7,1,1,1,1] => 604800
[6,5] => 518400
[6,4,1] => 259200
[6,3,2] => 207360
[6,3,1,1] => 207360
[6,2,2,1] => 207360
[6,2,1,1,1] => 259200
[6,1,1,1,1,1] => 518400
[5,5,1] => 259200
[5,4,2] => 172800
[5,4,1,1] => 172800
[5,3,3] => 172800
[5,3,2,1] => 138240
[5,3,1,1,1] => 172800
[5,2,2,2] => 172800
[5,2,2,1,1] => 172800
[5,2,1,1,1,1] => 259200
[5,1,1,1,1,1,1] => 604800
[4,4,3] => 172800
[4,4,2,1] => 138240
[4,4,1,1,1] => 172800
[4,3,3,1] => 138240
[4,3,2,2] => 138240
[4,3,2,1,1] => 138240
[4,3,1,1,1,1] => 207360
[4,2,2,2,1] => 172800
[4,2,2,1,1,1] => 207360
[4,2,1,1,1,1,1] => 362880
[4,1,1,1,1,1,1,1] => 967680
[3,3,3,2] => 172800
[3,3,3,1,1] => 172800
[3,3,2,2,1] => 172800
[3,3,2,1,1,1] => 207360
[3,3,1,1,1,1,1] => 362880
[3,2,2,2,2] => 259200
[3,2,2,2,1,1] => 259200
[3,2,2,1,1,1,1] => 362880
[3,2,1,1,1,1,1,1] => 725760
[3,1,1,1,1,1,1,1,1] => 2177280
[2,2,2,2,2,1] => 518400
[2,2,2,2,1,1,1] => 604800
[2,2,2,1,1,1,1,1] => 967680
[2,2,1,1,1,1,1,1,1] => 2177280
[2,1,1,1,1,1,1,1,1,1] => 7257600
[1,1,1,1,1,1,1,1,1,1,1] => 39916800
[12] => 479001600
[11,1] => 79833600
[10,2] => 21772800
[10,1,1] => 21772800
[9,3] => 8709120
[9,2,1] => 6531840
[9,1,1,1] => 8709120
[8,4] => 4838400
[8,3,1] => 2903040
[8,2,2] => 2903040
[8,2,1,1] => 2903040
[8,1,1,1,1] => 4838400
[7,5] => 3628800
[7,4,1] => 1814400
[7,3,2] => 1451520
[7,3,1,1] => 1451520
[7,2,2,1] => 1451520
[7,2,1,1,1] => 1814400
[7,1,1,1,1,1] => 3628800
[6,6] => 3628800
[6,5,1] => 1555200
[6,4,2] => 1036800
[6,4,1,1] => 1036800
[6,3,3] => 1036800
[6,3,2,1] => 829440
[6,3,1,1,1] => 1036800
[6,2,2,2] => 1036800
[6,2,2,1,1] => 1036800
[6,2,1,1,1,1] => 1555200
[6,1,1,1,1,1,1] => 3628800
[5,5,2] => 1036800
[5,5,1,1] => 1036800
[5,4,3] => 864000
[5,4,2,1] => 691200
[5,4,1,1,1] => 864000
[5,3,3,1] => 691200
[5,3,2,2] => 691200
[5,3,2,1,1] => 691200
[5,3,1,1,1,1] => 1036800
[5,2,2,2,1] => 864000
[5,2,2,1,1,1] => 1036800
[5,2,1,1,1,1,1] => 1814400
[5,1,1,1,1,1,1,1] => 4838400
[4,4,4] => 1036800
[4,4,3,1] => 691200
[4,4,2,2] => 691200
[4,4,2,1,1] => 691200
[4,4,1,1,1,1] => 1036800
[4,3,3,2] => 691200
[4,3,3,1,1] => 691200
[4,3,2,2,1] => 691200
[4,3,2,1,1,1] => 829440
[4,3,1,1,1,1,1] => 1451520
[4,2,2,2,2] => 1036800
[4,2,2,2,1,1] => 1036800
[4,2,2,1,1,1,1] => 1451520
[4,2,1,1,1,1,1,1] => 2903040
[4,1,1,1,1,1,1,1,1] => 8709120
[3,3,3,3] => 1036800
[3,3,3,2,1] => 864000
[3,3,3,1,1,1] => 1036800
[3,3,2,2,2] => 1036800
[3,3,2,2,1,1] => 1036800
[3,3,2,1,1,1,1] => 1451520
[3,3,1,1,1,1,1,1] => 2903040
[3,2,2,2,2,1] => 1555200
[3,2,2,2,1,1,1] => 1814400
[3,2,2,1,1,1,1,1] => 2903040
[3,2,1,1,1,1,1,1,1] => 6531840
[3,1,1,1,1,1,1,1,1,1] => 21772800
[2,2,2,2,2,2] => 3628800
[2,2,2,2,2,1,1] => 3628800
[2,2,2,2,1,1,1,1] => 4838400
[2,2,2,1,1,1,1,1,1] => 8709120
[2,2,1,1,1,1,1,1,1,1] => 21772800
[2,1,1,1,1,1,1,1,1,1,1] => 79833600
[1,1,1,1,1,1,1,1,1,1,1,1] => 479001600
[12,1] => 958003200
[11,2] => 239500800
[11,1,1] => 239500800
[10,3] => 87091200
[10,2,1] => 65318400
[10,1,1,1] => 87091200
[9,4] => 43545600
[9,3,1] => 26127360
[9,2,2] => 26127360
[9,2,1,1] => 26127360
[9,1,1,1,1] => 43545600
[8,5] => 29030400
[8,4,1] => 14515200
[8,3,2] => 11612160
[8,3,1,1] => 11612160
[8,2,2,1] => 11612160
[8,2,1,1,1] => 14515200
[8,1,1,1,1,1] => 29030400
[7,6] => 25401600
[7,5,1] => 10886400
[7,4,2] => 7257600
[7,4,1,1] => 7257600
[7,3,3] => 7257600
[7,3,2,1] => 5806080
[7,3,1,1,1] => 7257600
[7,2,2,2] => 7257600
[7,2,2,1,1] => 7257600
[7,2,1,1,1,1] => 10886400
[7,1,1,1,1,1,1] => 25401600
[6,6,1] => 10886400
[6,5,2] => 6220800
[6,5,1,1] => 6220800
[6,4,3] => 5184000
[6,4,2,1] => 4147200
[6,4,1,1,1] => 5184000
[6,3,3,1] => 4147200
[6,3,2,2] => 4147200
[6,3,2,1,1] => 4147200
[6,3,1,1,1,1] => 6220800
[6,2,2,2,1] => 5184000
[6,2,2,1,1,1] => 6220800
[6,2,1,1,1,1,1] => 10886400
[6,1,1,1,1,1,1,1] => 29030400
[5,5,3] => 5184000
[5,5,2,1] => 4147200
[5,5,1,1,1] => 5184000
[5,4,4] => 5184000
[5,4,3,1] => 3456000
[5,4,2,2] => 3456000
[5,4,2,1,1] => 3456000
[5,4,1,1,1,1] => 5184000
[5,3,3,2] => 3456000
[5,3,3,1,1] => 3456000
[5,3,2,2,1] => 3456000
[5,3,2,1,1,1] => 4147200
[5,3,1,1,1,1,1] => 7257600
[5,2,2,2,2] => 5184000
[5,2,2,2,1,1] => 5184000
[5,2,2,1,1,1,1] => 7257600
[5,2,1,1,1,1,1,1] => 14515200
[5,1,1,1,1,1,1,1,1] => 43545600
[4,4,4,1] => 4147200
[4,4,3,2] => 3456000
[4,4,3,1,1] => 3456000
[4,4,2,2,1] => 3456000
[4,4,2,1,1,1] => 4147200
[4,4,1,1,1,1,1] => 7257600
[4,3,3,3] => 4147200
[4,3,3,2,1] => 3456000
[4,3,3,1,1,1] => 4147200
[4,3,2,2,2] => 4147200
[4,3,2,2,1,1] => 4147200
[4,3,2,1,1,1,1] => 5806080
[4,3,1,1,1,1,1,1] => 11612160
[4,2,2,2,2,1] => 6220800
[4,2,2,2,1,1,1] => 7257600
[4,2,2,1,1,1,1,1] => 11612160
[4,2,1,1,1,1,1,1,1] => 26127360
[4,1,1,1,1,1,1,1,1,1] => 87091200
[3,3,3,3,1] => 5184000
[3,3,3,2,2] => 5184000
[3,3,3,2,1,1] => 5184000
[3,3,3,1,1,1,1] => 7257600
[3,3,2,2,2,1] => 6220800
[3,3,2,2,1,1,1] => 7257600
[3,3,2,1,1,1,1,1] => 11612160
[3,3,1,1,1,1,1,1,1] => 26127360
[3,2,2,2,2,2] => 10886400
[3,2,2,2,2,1,1] => 10886400
[3,2,2,2,1,1,1,1] => 14515200
[3,2,2,1,1,1,1,1,1] => 26127360
[3,2,1,1,1,1,1,1,1,1] => 65318400
[3,1,1,1,1,1,1,1,1,1,1] => 239500800
[2,2,2,2,2,2,1] => 25401600
[2,2,2,2,2,1,1,1] => 29030400
[2,2,2,2,1,1,1,1,1] => 43545600
[2,2,2,1,1,1,1,1,1,1] => 87091200
[2,2,1,1,1,1,1,1,1,1,1] => 239500800
[2,1,1,1,1,1,1,1,1,1,1,1] => 958003200
[11,3] => 958003200
[11,2,1] => 718502400
[11,1,1,1] => 958003200
[10,4] => 435456000
[10,3,1] => 261273600
[10,2,2] => 261273600
[10,2,1,1] => 261273600
[10,1,1,1,1] => 435456000
[9,5] => 261273600
[9,4,1] => 130636800
[9,3,2] => 104509440
[9,3,1,1] => 104509440
[9,2,2,1] => 104509440
[9,2,1,1,1] => 130636800
[9,1,1,1,1,1] => 261273600
[8,6] => 203212800
[8,5,1] => 87091200
[8,4,2] => 58060800
[8,4,1,1] => 58060800
[8,3,3] => 58060800
[8,3,2,1] => 46448640
[8,3,1,1,1] => 58060800
[8,2,2,2] => 58060800
[8,2,2,1,1] => 58060800
[8,2,1,1,1,1] => 87091200
[8,1,1,1,1,1,1] => 203212800
[7,7] => 203212800
[7,6,1] => 76204800
[7,5,2] => 43545600
[7,5,1,1] => 43545600
[7,4,3] => 36288000
[7,4,2,1] => 29030400
[7,4,1,1,1] => 36288000
[7,3,3,1] => 29030400
[7,3,2,2] => 29030400
[7,3,2,1,1] => 29030400
[7,3,1,1,1,1] => 43545600
[7,2,2,2,1] => 36288000
[7,2,2,1,1,1] => 43545600
[7,2,1,1,1,1,1] => 76204800
[7,1,1,1,1,1,1,1] => 203212800
[6,6,2] => 43545600
[6,6,1,1] => 43545600
[6,5,3] => 31104000
[6,5,2,1] => 24883200
[6,5,1,1,1] => 31104000
[6,4,4] => 31104000
[6,4,3,1] => 20736000
[6,4,2,2] => 20736000
[6,4,2,1,1] => 20736000
[6,4,1,1,1,1] => 31104000
[6,3,3,2] => 20736000
[6,3,3,1,1] => 20736000
[6,3,2,2,1] => 20736000
[6,3,2,1,1,1] => 24883200
[6,3,1,1,1,1,1] => 43545600
[6,2,2,2,2] => 31104000
[6,2,2,2,1,1] => 31104000
[6,2,2,1,1,1,1] => 43545600
[6,2,1,1,1,1,1,1] => 87091200
[6,1,1,1,1,1,1,1,1] => 261273600
[5,5,4] => 31104000
[5,5,3,1] => 20736000
[5,5,2,2] => 20736000
[5,5,2,1,1] => 20736000
[5,5,1,1,1,1] => 31104000
[5,4,4,1] => 20736000
[5,4,3,2] => 17280000
[5,4,3,1,1] => 17280000
[5,4,2,2,1] => 17280000
[5,4,2,1,1,1] => 20736000
[5,4,1,1,1,1,1] => 36288000
[5,3,3,3] => 20736000
[5,3,3,2,1] => 17280000
[5,3,3,1,1,1] => 20736000
[5,3,2,2,2] => 20736000
[5,3,2,2,1,1] => 20736000
[5,3,2,1,1,1,1] => 29030400
[5,3,1,1,1,1,1,1] => 58060800
[5,2,2,2,2,1] => 31104000
[5,2,2,2,1,1,1] => 36288000
[5,2,2,1,1,1,1,1] => 58060800
[5,2,1,1,1,1,1,1,1] => 130636800
[5,1,1,1,1,1,1,1,1,1] => 435456000
[4,4,4,2] => 20736000
[4,4,4,1,1] => 20736000
[4,4,3,3] => 20736000
[4,4,3,2,1] => 17280000
[4,4,3,1,1,1] => 20736000
[4,4,2,2,2] => 20736000
[4,4,2,2,1,1] => 20736000
[4,4,2,1,1,1,1] => 29030400
[4,4,1,1,1,1,1,1] => 58060800
[4,3,3,3,1] => 20736000
[4,3,3,2,2] => 20736000
[4,3,3,2,1,1] => 20736000
[4,3,3,1,1,1,1] => 29030400
[4,3,2,2,2,1] => 24883200
[4,3,2,2,1,1,1] => 29030400
[4,3,2,1,1,1,1,1] => 46448640
[4,3,1,1,1,1,1,1,1] => 104509440
[4,2,2,2,2,2] => 43545600
[4,2,2,2,2,1,1] => 43545600
[4,2,2,2,1,1,1,1] => 58060800
[4,2,2,1,1,1,1,1,1] => 104509440
[4,2,1,1,1,1,1,1,1,1] => 261273600
[4,1,1,1,1,1,1,1,1,1,1] => 958003200
[3,3,3,3,2] => 31104000
[3,3,3,3,1,1] => 31104000
[3,3,3,2,2,1] => 31104000
[3,3,3,2,1,1,1] => 36288000
[3,3,3,1,1,1,1,1] => 58060800
[3,3,2,2,2,2] => 43545600
[3,3,2,2,2,1,1] => 43545600
[3,3,2,2,1,1,1,1] => 58060800
[3,3,2,1,1,1,1,1,1] => 104509440
[3,3,1,1,1,1,1,1,1,1] => 261273600
[3,2,2,2,2,2,1] => 76204800
[3,2,2,2,2,1,1,1] => 87091200
[3,2,2,2,1,1,1,1,1] => 130636800
[3,2,2,1,1,1,1,1,1,1] => 261273600
[3,2,1,1,1,1,1,1,1,1,1] => 718502400
[2,2,2,2,2,2,2] => 203212800
[2,2,2,2,2,2,1,1] => 203212800
[2,2,2,2,2,1,1,1,1] => 261273600
[2,2,2,2,1,1,1,1,1,1] => 435456000
[2,2,2,1,1,1,1,1,1,1,1] => 958003200
[10,4,1] => 1306368000
[10,3,2] => 1045094400
[10,3,1,1] => 1045094400
[10,2,2,1] => 1045094400
[10,2,1,1,1] => 1306368000
[9,6] => 1828915200
[9,5,1] => 783820800
[9,4,2] => 522547200
[9,4,1,1] => 522547200
[9,3,3] => 522547200
[9,3,2,1] => 418037760
[9,3,1,1,1] => 522547200
[9,2,2,2] => 522547200
[9,2,2,1,1] => 522547200
[9,2,1,1,1,1] => 783820800
[9,1,1,1,1,1,1] => 1828915200
[8,7] => 1625702400
[8,6,1] => 609638400
[8,5,2] => 348364800
[8,5,1,1] => 348364800
[8,4,3] => 290304000
[8,4,2,1] => 232243200
[8,4,1,1,1] => 290304000
[8,3,3,1] => 232243200
[8,3,2,2] => 232243200
[8,3,2,1,1] => 232243200
[8,3,1,1,1,1] => 348364800
[8,2,2,2,1] => 290304000
[8,2,2,1,1,1] => 348364800
[8,2,1,1,1,1,1] => 609638400
[8,1,1,1,1,1,1,1] => 1625702400
[7,7,1] => 609638400
[7,6,2] => 304819200
[7,6,1,1] => 304819200
[7,5,3] => 217728000
[7,5,2,1] => 174182400
[7,5,1,1,1] => 217728000
[7,4,4] => 217728000
[7,4,3,1] => 145152000
[7,4,2,2] => 145152000
[7,4,2,1,1] => 145152000
[7,4,1,1,1,1] => 217728000
[7,3,3,2] => 145152000
[7,3,3,1,1] => 145152000
[7,3,2,2,1] => 145152000
[7,3,2,1,1,1] => 174182400
[7,3,1,1,1,1,1] => 304819200
[7,2,2,2,2] => 217728000
[7,2,2,2,1,1] => 217728000
[7,2,2,1,1,1,1] => 304819200
[7,2,1,1,1,1,1,1] => 609638400
[7,1,1,1,1,1,1,1,1] => 1828915200
[6,6,3] => 217728000
[6,6,2,1] => 174182400
[6,6,1,1,1] => 217728000
[6,5,4] => 186624000
[6,5,3,1] => 124416000
[6,5,2,2] => 124416000
[6,5,2,1,1] => 124416000
[6,5,1,1,1,1] => 186624000
[6,4,4,1] => 124416000
[6,4,3,2] => 103680000
[6,4,3,1,1] => 103680000
[6,4,2,2,1] => 103680000
[6,4,2,1,1,1] => 124416000
[6,4,1,1,1,1,1] => 217728000
[6,3,3,3] => 124416000
[6,3,3,2,1] => 103680000
[6,3,3,1,1,1] => 124416000
[6,3,2,2,2] => 124416000
[6,3,2,2,1,1] => 124416000
[6,3,2,1,1,1,1] => 174182400
[6,3,1,1,1,1,1,1] => 348364800
[6,2,2,2,2,1] => 186624000
[6,2,2,2,1,1,1] => 217728000
[6,2,2,1,1,1,1,1] => 348364800
[6,2,1,1,1,1,1,1,1] => 783820800
[5,5,5] => 217728000
[5,5,4,1] => 124416000
[5,5,3,2] => 103680000
[5,5,3,1,1] => 103680000
[5,5,2,2,1] => 103680000
[5,5,2,1,1,1] => 124416000
[5,5,1,1,1,1,1] => 217728000
[5,4,4,2] => 103680000
[5,4,4,1,1] => 103680000
[5,4,3,3] => 103680000
[5,4,3,2,1] => 86400000
[5,4,3,1,1,1] => 103680000
[5,4,2,2,2] => 103680000
[5,4,2,2,1,1] => 103680000
[5,4,2,1,1,1,1] => 145152000
[5,4,1,1,1,1,1,1] => 290304000
[5,3,3,3,1] => 103680000
[5,3,3,2,2] => 103680000
[5,3,3,2,1,1] => 103680000
[5,3,3,1,1,1,1] => 145152000
[5,3,2,2,2,1] => 124416000
[5,3,2,2,1,1,1] => 145152000
[5,3,2,1,1,1,1,1] => 232243200
[5,3,1,1,1,1,1,1,1] => 522547200
[5,2,2,2,2,2] => 217728000
[5,2,2,2,2,1,1] => 217728000
[5,2,2,2,1,1,1,1] => 290304000
[5,2,2,1,1,1,1,1,1] => 522547200
[5,2,1,1,1,1,1,1,1,1] => 1306368000
[4,4,4,3] => 124416000
[4,4,4,2,1] => 103680000
[4,4,4,1,1,1] => 124416000
[4,4,3,3,1] => 103680000
[4,4,3,2,2] => 103680000
[4,4,3,2,1,1] => 103680000
[4,4,3,1,1,1,1] => 145152000
[4,4,2,2,2,1] => 124416000
[4,4,2,2,1,1,1] => 145152000
[4,4,2,1,1,1,1,1] => 232243200
[4,4,1,1,1,1,1,1,1] => 522547200
[4,3,3,3,2] => 124416000
[4,3,3,3,1,1] => 124416000
[4,3,3,2,2,1] => 124416000
[4,3,3,2,1,1,1] => 145152000
[4,3,3,1,1,1,1,1] => 232243200
[4,3,2,2,2,2] => 174182400
[4,3,2,2,2,1,1] => 174182400
[4,3,2,2,1,1,1,1] => 232243200
[4,3,2,1,1,1,1,1,1] => 418037760
[4,3,1,1,1,1,1,1,1,1] => 1045094400
[4,2,2,2,2,2,1] => 304819200
[4,2,2,2,2,1,1,1] => 348364800
[4,2,2,2,1,1,1,1,1] => 522547200
[4,2,2,1,1,1,1,1,1,1] => 1045094400
[3,3,3,3,3] => 217728000
[3,3,3,3,2,1] => 186624000
[3,3,3,3,1,1,1] => 217728000
[3,3,3,2,2,2] => 217728000
[3,3,3,2,2,1,1] => 217728000
[3,3,3,2,1,1,1,1] => 290304000
[3,3,3,1,1,1,1,1,1] => 522547200
[3,3,2,2,2,2,1] => 304819200
[3,3,2,2,2,1,1,1] => 348364800
[3,3,2,2,1,1,1,1,1] => 522547200
[3,3,2,1,1,1,1,1,1,1] => 1045094400
[3,2,2,2,2,2,2] => 609638400
[3,2,2,2,2,2,1,1] => 609638400
[3,2,2,2,2,1,1,1,1] => 783820800
[3,2,2,2,1,1,1,1,1,1] => 1306368000
[2,2,2,2,2,2,2,1] => 1625702400
[2,2,2,2,2,2,1,1,1] => 1828915200
[9,4,2,1] => 2090188800
[9,3,3,1] => 2090188800
[9,3,2,2] => 2090188800
[9,3,2,1,1] => 2090188800
[8,5,3] => 1741824000
[8,5,2,1] => 1393459200
[8,5,1,1,1] => 1741824000
[8,4,4] => 1741824000
[8,4,3,1] => 1161216000
[8,4,2,2] => 1161216000
[8,4,2,1,1] => 1161216000
[8,4,1,1,1,1] => 1741824000
[8,3,3,2] => 1161216000
[8,3,3,1,1] => 1161216000
[8,3,2,2,1] => 1161216000
[8,3,2,1,1,1] => 1393459200
[8,2,2,2,2] => 1741824000
[8,2,2,2,1,1] => 1741824000
[7,6,3] => 1524096000
[7,6,2,1] => 1219276800
[7,6,1,1,1] => 1524096000
[7,5,4] => 1306368000
[7,5,3,1] => 870912000
[7,5,2,2] => 870912000
[7,5,2,1,1] => 870912000
[7,5,1,1,1,1] => 1306368000
[7,4,4,1] => 870912000
[7,4,3,2] => 725760000
[7,4,3,1,1] => 725760000
[7,4,2,2,1] => 725760000
[7,4,2,1,1,1] => 870912000
[7,4,1,1,1,1,1] => 1524096000
[7,3,3,3] => 870912000
[7,3,3,2,1] => 725760000
[7,3,3,1,1,1] => 870912000
[7,3,2,2,2] => 870912000
[7,3,2,2,1,1] => 870912000
[7,3,2,1,1,1,1] => 1219276800
[7,2,2,2,2,1] => 1306368000
[7,2,2,2,1,1,1] => 1524096000
[6,6,4] => 1306368000
[6,6,3,1] => 870912000
[6,6,2,2] => 870912000
[6,6,2,1,1] => 870912000
[6,6,1,1,1,1] => 1306368000
[6,5,5] => 1306368000
[6,5,4,1] => 746496000
[6,5,3,2] => 622080000
[6,5,3,1,1] => 622080000
[6,5,2,2,1] => 622080000
[6,5,2,1,1,1] => 746496000
[6,5,1,1,1,1,1] => 1306368000
[6,4,4,2] => 622080000
[6,4,4,1,1] => 622080000
[6,4,3,3] => 622080000
[6,4,3,2,1] => 518400000
[6,4,3,1,1,1] => 622080000
[6,4,2,2,2] => 622080000
[6,4,2,2,1,1] => 622080000
[6,4,2,1,1,1,1] => 870912000
[6,4,1,1,1,1,1,1] => 1741824000
[6,3,3,3,1] => 622080000
[6,3,3,2,2] => 622080000
[6,3,3,2,1,1] => 622080000
[6,3,3,1,1,1,1] => 870912000
[6,3,2,2,2,1] => 746496000
[6,3,2,2,1,1,1] => 870912000
[6,3,2,1,1,1,1,1] => 1393459200
[6,2,2,2,2,2] => 1306368000
[6,2,2,2,2,1,1] => 1306368000
[6,2,2,2,1,1,1,1] => 1741824000
[5,5,5,1] => 870912000
[5,5,4,2] => 622080000
[5,5,4,1,1] => 622080000
[5,5,3,3] => 622080000
[5,5,3,2,1] => 518400000
[5,5,3,1,1,1] => 622080000
[5,5,2,2,2] => 622080000
[5,5,2,2,1,1] => 622080000
[5,5,2,1,1,1,1] => 870912000
[5,5,1,1,1,1,1,1] => 1741824000
[5,4,4,3] => 622080000
[5,4,4,2,1] => 518400000
[5,4,4,1,1,1] => 622080000
[5,4,3,3,1] => 518400000
[5,4,3,2,2] => 518400000
[5,4,3,2,1,1] => 518400000
[5,4,3,1,1,1,1] => 725760000
[5,4,2,2,2,1] => 622080000
[5,4,2,2,1,1,1] => 725760000
[5,4,2,1,1,1,1,1] => 1161216000
[5,3,3,3,2] => 622080000
[5,3,3,3,1,1] => 622080000
[5,3,3,2,2,1] => 622080000
[5,3,3,2,1,1,1] => 725760000
[5,3,3,1,1,1,1,1] => 1161216000
[5,3,2,2,2,2] => 870912000
[5,3,2,2,2,1,1] => 870912000
[5,3,2,2,1,1,1,1] => 1161216000
[5,3,2,1,1,1,1,1,1] => 2090188800
[5,2,2,2,2,2,1] => 1524096000
[5,2,2,2,2,1,1,1] => 1741824000
[4,4,4,4] => 870912000
[4,4,4,3,1] => 622080000
[4,4,4,2,2] => 622080000
[4,4,4,2,1,1] => 622080000
[4,4,4,1,1,1,1] => 870912000
[4,4,3,3,2] => 622080000
[4,4,3,3,1,1] => 622080000
[4,4,3,2,2,1] => 622080000
[4,4,3,2,1,1,1] => 725760000
[4,4,3,1,1,1,1,1] => 1161216000
[4,4,2,2,2,2] => 870912000
[4,4,2,2,2,1,1] => 870912000
[4,4,2,2,1,1,1,1] => 1161216000
[4,4,2,1,1,1,1,1,1] => 2090188800
[4,3,3,3,3] => 870912000
[4,3,3,3,2,1] => 746496000
[4,3,3,3,1,1,1] => 870912000
[4,3,3,2,2,2] => 870912000
[4,3,3,2,2,1,1] => 870912000
[4,3,3,2,1,1,1,1] => 1161216000
[4,3,3,1,1,1,1,1,1] => 2090188800
[4,3,2,2,2,2,1] => 1219276800
[4,3,2,2,2,1,1,1] => 1393459200
[4,3,2,2,1,1,1,1,1] => 2090188800
[3,3,3,3,3,1] => 1306368000
[3,3,3,3,2,2] => 1306368000
[3,3,3,3,2,1,1] => 1306368000
[3,3,3,3,1,1,1,1] => 1741824000
[3,3,3,2,2,2,1] => 1524096000
[3,3,3,2,2,1,1,1] => 1741824000
-----------------------------------------------------------------------------
Created: Mar 29, 2019 at 11:57 by Christian Stump
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Last Updated: Mar 29, 2019 at 11:57 by Christian Stump