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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. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St001714
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The number of subpartitions of an integer partition that do not dominate the conjugate subpartition.
In particular, partitions with statistic $0$ are wide partitions.
-----------------------------------------------------------------------------
References: [1] Chow, T. Y., Fan, C. K., Goemans, M. X., Vondrak, J. Wide partitions, Latin tableaux, and Rota's basis conjecture [[MathSciNet:2001618]]
-----------------------------------------------------------------------------
Code:
def statistic(la):
c = 0
for mu in Subsets(la, submultiset=True):
mu = Partition(mu)
if not mu.dominates(mu.conjugate()):
c += 1
return c
-----------------------------------------------------------------------------
Statistic values:
[1] => 0
[2] => 0
[1,1] => 1
[3] => 0
[2,1] => 0
[1,1,1] => 2
[4] => 0
[3,1] => 0
[2,2] => 0
[2,1,1] => 2
[1,1,1,1] => 3
[5] => 0
[4,1] => 0
[3,2] => 0
[3,1,1] => 1
[2,2,1] => 1
[2,1,1,1] => 4
[1,1,1,1,1] => 4
[6] => 0
[5,1] => 0
[4,2] => 0
[4,1,1] => 1
[3,3] => 0
[3,2,1] => 0
[3,1,1,1] => 3
[2,2,2] => 1
[2,2,1,1] => 4
[2,1,1,1,1] => 6
[1,1,1,1,1,1] => 5
[7] => 0
[6,1] => 0
[5,2] => 0
[5,1,1] => 1
[4,3] => 0
[4,2,1] => 0
[4,1,1,1] => 2
[3,3,1] => 0
[3,2,2] => 1
[3,2,1,1] => 3
[3,1,1,1,1] => 5
[2,2,2,1] => 3
[2,2,1,1,1] => 7
[2,1,1,1,1,1] => 8
[1,1,1,1,1,1,1] => 6
[8] => 0
[7,1] => 0
[6,2] => 0
[6,1,1] => 1
[5,3] => 0
[5,2,1] => 0
[5,1,1,1] => 2
[4,4] => 0
[4,3,1] => 0
[4,2,2] => 0
[4,2,1,1] => 2
[4,1,1,1,1] => 4
[3,3,2] => 0
[3,3,1,1] => 2
[3,2,2,1] => 3
[3,2,1,1,1] => 7
[3,1,1,1,1,1] => 7
[2,2,2,2] => 2
[2,2,2,1,1] => 7
[2,2,1,1,1,1] => 10
[2,1,1,1,1,1,1] => 10
[1,1,1,1,1,1,1,1] => 7
[9] => 0
[8,1] => 0
[7,2] => 0
[7,1,1] => 1
[6,3] => 0
[6,2,1] => 0
[6,1,1,1] => 2
[5,4] => 0
[5,3,1] => 0
[5,2,2] => 0
[5,2,1,1] => 2
[5,1,1,1,1] => 3
[4,4,1] => 0
[4,3,2] => 0
[4,3,1,1] => 1
[4,2,2,1] => 2
[4,2,1,1,1] => 5
[4,1,1,1,1,1] => 6
[3,3,3] => 0
[3,3,2,1] => 1
[3,3,1,1,1] => 5
[3,2,2,2] => 3
[3,2,2,1,1] => 8
[3,2,1,1,1,1] => 11
[3,1,1,1,1,1,1] => 9
[2,2,2,2,1] => 5
[2,2,2,1,1,1] => 11
[2,2,1,1,1,1,1] => 13
[2,1,1,1,1,1,1,1] => 12
[1,1,1,1,1,1,1,1,1] => 8
[10] => 0
[9,1] => 0
[8,2] => 0
[8,1,1] => 1
[7,3] => 0
[7,2,1] => 0
[7,1,1,1] => 2
[6,4] => 0
[6,3,1] => 0
[6,2,2] => 0
[6,2,1,1] => 2
[6,1,1,1,1] => 3
[5,5] => 0
[5,4,1] => 0
[5,3,2] => 0
[5,3,1,1] => 1
[5,2,2,1] => 1
[5,2,1,1,1] => 4
[5,1,1,1,1,1] => 5
[4,4,2] => 0
[4,4,1,1] => 1
[4,3,3] => 0
[4,3,2,1] => 0
[4,3,1,1,1] => 4
[4,2,2,2] => 2
[4,2,2,1,1] => 6
[4,2,1,1,1,1] => 9
[4,1,1,1,1,1,1] => 8
[3,3,3,1] => 1
[3,3,2,2] => 2
[3,3,2,1,1] => 6
[3,3,1,1,1,1] => 8
[3,2,2,2,1] => 7
[3,2,2,1,1,1] => 14
[3,2,1,1,1,1,1] => 15
[3,1,1,1,1,1,1,1] => 11
[2,2,2,2,2] => 3
[2,2,2,2,1,1] => 10
[2,2,2,1,1,1,1] => 15
[2,2,1,1,1,1,1,1] => 16
[2,1,1,1,1,1,1,1,1] => 14
[1,1,1,1,1,1,1,1,1,1] => 9
[11] => 0
[10,1] => 0
[9,2] => 0
[9,1,1] => 1
[8,3] => 0
[8,2,1] => 0
[8,1,1,1] => 2
[7,4] => 0
[7,3,1] => 0
[7,2,2] => 0
[7,2,1,1] => 2
[7,1,1,1,1] => 3
[6,5] => 0
[6,4,1] => 0
[6,3,2] => 0
[6,3,1,1] => 1
[6,2,2,1] => 1
[6,2,1,1,1] => 4
[6,1,1,1,1,1] => 4
[5,5,1] => 0
[5,4,2] => 0
[5,4,1,1] => 1
[5,3,3] => 0
[5,3,2,1] => 0
[5,3,1,1,1] => 3
[5,2,2,2] => 2
[5,2,2,1,1] => 5
[5,2,1,1,1,1] => 7
[5,1,1,1,1,1,1] => 7
[4,4,3] => 0
[4,4,2,1] => 0
[4,4,1,1,1] => 3
[4,3,3,1] => 0
[4,3,2,2] => 2
[4,3,2,1,1] => 4
[4,3,1,1,1,1] => 8
[4,2,2,2,1] => 6
[4,2,2,1,1,1] => 11
[4,2,1,1,1,1,1] => 13
[4,1,1,1,1,1,1,1] => 10
[3,3,3,2] => 1
[3,3,3,1,1] => 4
[3,3,2,2,1] => 6
[3,3,2,1,1,1] => 12
[3,3,1,1,1,1,1] => 11
[3,2,2,2,2] => 5
[3,2,2,2,1,1] => 14
[3,2,2,1,1,1,1] => 20
[3,2,1,1,1,1,1,1] => 19
[3,1,1,1,1,1,1,1,1] => 13
[2,2,2,2,2,1] => 7
[2,2,2,2,1,1,1] => 15
[2,2,2,1,1,1,1,1] => 19
[2,2,1,1,1,1,1,1,1] => 19
[2,1,1,1,1,1,1,1,1,1] => 16
[1,1,1,1,1,1,1,1,1,1,1] => 10
[12] => 0
[11,1] => 0
[10,2] => 0
[10,1,1] => 1
[9,3] => 0
[9,2,1] => 0
[9,1,1,1] => 2
[8,4] => 0
[8,3,1] => 0
[8,2,2] => 0
[8,2,1,1] => 2
[8,1,1,1,1] => 3
[7,5] => 0
[7,4,1] => 0
[7,3,2] => 0
[7,3,1,1] => 1
[7,2,2,1] => 1
[7,2,1,1,1] => 4
[7,1,1,1,1,1] => 4
[6,6] => 0
[6,5,1] => 0
[6,4,2] => 0
[6,4,1,1] => 1
[6,3,3] => 0
[6,3,2,1] => 0
[6,3,1,1,1] => 3
[6,2,2,2] => 1
[6,2,2,1,1] => 4
[6,2,1,1,1,1] => 6
[6,1,1,1,1,1,1] => 6
[5,5,2] => 0
[5,5,1,1] => 1
[5,4,3] => 0
[5,4,2,1] => 0
[5,4,1,1,1] => 2
[5,3,3,1] => 0
[5,3,2,2] => 1
[5,3,2,1,1] => 3
[5,3,1,1,1,1] => 6
[5,2,2,2,1] => 5
[5,2,2,1,1,1] => 9
[5,2,1,1,1,1,1] => 11
[5,1,1,1,1,1,1,1] => 9
[4,4,4] => 0
[4,4,3,1] => 0
[4,4,2,2] => 0
[4,4,2,1,1] => 3
[4,4,1,1,1,1] => 6
[4,3,3,2] => 1
[4,3,3,1,1] => 3
[4,3,2,2,1] => 6
[4,3,2,1,1,1] => 11
[4,3,1,1,1,1,1] => 12
[4,2,2,2,2] => 4
[4,2,2,2,1,1] => 12
[4,2,2,1,1,1,1] => 17
[4,2,1,1,1,1,1,1] => 17
[4,1,1,1,1,1,1,1,1] => 12
[3,3,3,3] => 1
[3,3,3,2,1] => 4
[3,3,3,1,1,1] => 8
[3,3,2,2,2] => 5
[3,3,2,2,1,1] => 14
[3,3,2,1,1,1,1] => 18
[3,3,1,1,1,1,1,1] => 14
[3,2,2,2,2,1] => 11
[3,2,2,2,1,1,1] => 22
[3,2,2,1,1,1,1,1] => 26
[3,2,1,1,1,1,1,1,1] => 23
[3,1,1,1,1,1,1,1,1,1] => 15
[2,2,2,2,2,2] => 4
[2,2,2,2,2,1,1] => 13
[2,2,2,2,1,1,1,1] => 20
[2,2,2,1,1,1,1,1,1] => 23
[2,2,1,1,1,1,1,1,1,1] => 22
[2,1,1,1,1,1,1,1,1,1,1] => 18
[1,1,1,1,1,1,1,1,1,1,1,1] => 11
[13] => 0
[12,1] => 0
[11,2] => 0
[11,1,1] => 1
[10,3] => 0
[10,2,1] => 0
[10,1,1,1] => 2
[9,4] => 0
[9,3,1] => 0
[9,2,2] => 0
[9,2,1,1] => 2
[9,1,1,1,1] => 3
[8,5] => 0
[8,4,1] => 0
[8,3,2] => 0
[8,3,1,1] => 1
[8,2,2,1] => 1
[8,2,1,1,1] => 4
[8,1,1,1,1,1] => 4
[7,6] => 0
[7,5,1] => 0
[7,4,2] => 0
[7,4,1,1] => 1
[7,3,3] => 0
[7,3,2,1] => 0
[7,3,1,1,1] => 3
[7,2,2,2] => 1
[7,2,2,1,1] => 4
[7,2,1,1,1,1] => 6
[7,1,1,1,1,1,1] => 5
[6,6,1] => 0
[6,5,2] => 0
[6,5,1,1] => 1
[6,4,3] => 0
[6,4,2,1] => 0
[6,4,1,1,1] => 2
[6,3,3,1] => 0
[6,3,2,2] => 1
[6,3,2,1,1] => 3
[6,3,1,1,1,1] => 5
[6,2,2,2,1] => 4
[6,2,2,1,1,1] => 8
[6,2,1,1,1,1,1] => 9
[6,1,1,1,1,1,1,1] => 8
[5,5,3] => 0
[5,5,2,1] => 0
[5,5,1,1,1] => 2
[5,4,4] => 0
[5,4,3,1] => 0
[5,4,2,2] => 0
[5,4,2,1,1] => 2
[5,4,1,1,1,1] => 5
[5,3,3,2] => 0
[5,3,3,1,1] => 2
[5,3,2,2,1] => 4
[5,3,2,1,1,1] => 8
[5,3,1,1,1,1,1] => 10
[5,2,2,2,2] => 4
[5,2,2,2,1,1] => 11
[5,2,2,1,1,1,1] => 14
[5,2,1,1,1,1,1,1] => 15
[5,1,1,1,1,1,1,1,1] => 11
[4,4,4,1] => 0
[4,4,3,2] => 0
[4,4,3,1,1] => 2
[4,4,2,2,1] => 3
[4,4,2,1,1,1] => 8
[4,4,1,1,1,1,1] => 9
[4,3,3,3] => 1
[4,3,3,2,1] => 3
[4,3,3,1,1,1] => 8
[4,3,2,2,2] => 6
[4,3,2,2,1,1] => 14
[4,3,2,1,1,1,1] => 19
[4,3,1,1,1,1,1,1] => 16
[4,2,2,2,2,1] => 10
[4,2,2,2,1,1,1] => 19
[4,2,2,1,1,1,1,1] => 23
[4,2,1,1,1,1,1,1,1] => 21
[4,1,1,1,1,1,1,1,1,1] => 14
[3,3,3,3,1] => 3
[3,3,3,2,2] => 4
[3,3,3,2,1,1] => 11
[3,3,3,1,1,1,1] => 12
[3,3,2,2,2,1] => 12
[3,3,2,2,1,1,1] => 23
[3,3,2,1,1,1,1,1] => 24
[3,3,1,1,1,1,1,1,1] => 17
[3,2,2,2,2,2] => 7
[3,2,2,2,2,1,1] => 20
[3,2,2,2,1,1,1,1] => 30
[3,2,2,1,1,1,1,1,1] => 32
[3,2,1,1,1,1,1,1,1,1] => 27
[3,1,1,1,1,1,1,1,1,1,1] => 17
[2,2,2,2,2,2,1] => 9
[2,2,2,2,2,1,1,1] => 19
[2,2,2,2,1,1,1,1,1] => 25
[2,2,2,1,1,1,1,1,1,1] => 27
[2,2,1,1,1,1,1,1,1,1,1] => 25
[2,1,1,1,1,1,1,1,1,1,1,1] => 20
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 12
[14] => 0
[13,1] => 0
[12,2] => 0
[12,1,1] => 1
[11,3] => 0
[11,2,1] => 0
[11,1,1,1] => 2
[10,4] => 0
[10,3,1] => 0
[10,2,2] => 0
[10,2,1,1] => 2
[10,1,1,1,1] => 3
[9,5] => 0
[9,4,1] => 0
[9,3,2] => 0
[9,3,1,1] => 1
[9,2,2,1] => 1
[9,2,1,1,1] => 4
[9,1,1,1,1,1] => 4
[8,6] => 0
[8,5,1] => 0
[8,4,2] => 0
[8,4,1,1] => 1
[8,3,3] => 0
[8,3,2,1] => 0
[8,3,1,1,1] => 3
[8,2,2,2] => 1
[8,2,2,1,1] => 4
[8,2,1,1,1,1] => 6
[8,1,1,1,1,1,1] => 5
[7,7] => 0
[7,6,1] => 0
[7,5,2] => 0
[7,5,1,1] => 1
[7,4,3] => 0
[7,4,2,1] => 0
[7,4,1,1,1] => 2
[7,3,3,1] => 0
[7,3,2,2] => 1
[7,3,2,1,1] => 3
[7,3,1,1,1,1] => 5
[7,2,2,2,1] => 3
[7,2,2,1,1,1] => 7
[7,2,1,1,1,1,1] => 8
[7,1,1,1,1,1,1,1] => 7
[6,6,2] => 0
[6,6,1,1] => 1
[6,5,3] => 0
[6,5,2,1] => 0
[6,5,1,1,1] => 2
[6,4,4] => 0
[6,4,3,1] => 0
[6,4,2,2] => 0
[6,4,2,1,1] => 2
[6,4,1,1,1,1] => 4
[6,3,3,2] => 0
[6,3,3,1,1] => 2
[6,3,2,2,1] => 3
[6,3,2,1,1,1] => 7
[6,3,1,1,1,1,1] => 8
[6,2,2,2,2] => 3
[6,2,2,2,1,1] => 9
[6,2,2,1,1,1,1] => 12
[6,2,1,1,1,1,1,1] => 13
[6,1,1,1,1,1,1,1,1] => 10
[5,5,4] => 0
[5,5,3,1] => 0
[5,5,2,2] => 0
[5,5,2,1,1] => 2
[5,5,1,1,1,1] => 4
[5,4,4,1] => 0
[5,4,3,2] => 0
[5,4,3,1,1] => 1
[5,4,2,2,1] => 2
[5,4,2,1,1,1] => 6
[5,4,1,1,1,1,1] => 9
[5,3,3,3] => 1
[5,3,3,2,1] => 2
[5,3,3,1,1,1] => 6
[5,3,2,2,2] => 5
[5,3,2,2,1,1] => 11
[5,3,2,1,1,1,1] => 15
[5,3,1,1,1,1,1,1] => 14
[5,2,2,2,2,1] => 9
[5,2,2,2,1,1,1] => 17
[5,2,2,1,1,1,1,1] => 20
[5,2,1,1,1,1,1,1,1] => 19
[5,1,1,1,1,1,1,1,1,1] => 13
[4,4,4,2] => 0
[4,4,4,1,1] => 2
[4,4,3,3] => 1
[4,4,3,2,1] => 1
[4,4,3,1,1,1] => 7
[4,4,2,2,2] => 3
[4,4,2,2,1,1] => 9
[4,4,2,1,1,1,1] => 14
[4,4,1,1,1,1,1,1] => 12
[4,3,3,3,1] => 3
[4,3,3,2,2] => 5
[4,3,3,2,1,1] => 11
[4,3,3,1,1,1,1] => 14
[4,3,2,2,2,1] => 14
[4,3,2,2,1,1,1] => 25
[4,3,2,1,1,1,1,1] => 27
[4,3,1,1,1,1,1,1,1] => 20
[4,2,2,2,2,2] => 6
[4,2,2,2,2,1,1] => 18
[4,2,2,2,1,1,1,1] => 27
[4,2,2,1,1,1,1,1,1] => 29
[4,2,1,1,1,1,1,1,1,1] => 25
[4,1,1,1,1,1,1,1,1,1,1] => 16
[3,3,3,3,2] => 3
[3,3,3,3,1,1] => 7
[3,3,3,2,2,1] => 11
[3,3,3,2,1,1,1] => 19
[3,3,3,1,1,1,1,1] => 16
[3,3,2,2,2,2] => 8
[3,3,2,2,2,1,1] => 23
[3,3,2,2,1,1,1,1] => 32
[3,3,2,1,1,1,1,1,1] => 30
[3,3,1,1,1,1,1,1,1,1] => 20
[3,2,2,2,2,2,1] => 15
[3,2,2,2,2,1,1,1] => 30
[3,2,2,2,1,1,1,1,1] => 38
[3,2,2,1,1,1,1,1,1,1] => 38
[3,2,1,1,1,1,1,1,1,1,1] => 31
[3,1,1,1,1,1,1,1,1,1,1,1] => 19
[2,2,2,2,2,2,2] => 5
[2,2,2,2,2,2,1,1] => 16
[2,2,2,2,2,1,1,1,1] => 25
[2,2,2,2,1,1,1,1,1,1] => 30
[2,2,2,1,1,1,1,1,1,1,1] => 31
[2,2,1,1,1,1,1,1,1,1,1,1] => 28
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 22
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 13
[15] => 0
[14,1] => 0
[13,2] => 0
[13,1,1] => 1
[12,3] => 0
[12,2,1] => 0
[12,1,1,1] => 2
[11,4] => 0
[11,3,1] => 0
[11,2,2] => 0
[11,2,1,1] => 2
[11,1,1,1,1] => 3
[10,5] => 0
[10,4,1] => 0
[10,3,2] => 0
[10,3,1,1] => 1
[10,2,2,1] => 1
[10,2,1,1,1] => 4
[10,1,1,1,1,1] => 4
[9,6] => 0
[9,5,1] => 0
[9,4,2] => 0
[9,4,1,1] => 1
[9,3,3] => 0
[9,3,2,1] => 0
[9,3,1,1,1] => 3
[9,2,2,2] => 1
[9,2,2,1,1] => 4
[9,2,1,1,1,1] => 6
[9,1,1,1,1,1,1] => 5
[8,7] => 0
[8,6,1] => 0
[8,5,2] => 0
[8,5,1,1] => 1
[8,4,3] => 0
[8,4,2,1] => 0
[8,4,1,1,1] => 2
[8,3,3,1] => 0
[8,3,2,2] => 1
[8,3,2,1,1] => 3
[8,3,1,1,1,1] => 5
[8,2,2,2,1] => 3
[8,2,2,1,1,1] => 7
[8,2,1,1,1,1,1] => 8
[8,1,1,1,1,1,1,1] => 6
[7,7,1] => 0
[7,6,2] => 0
[7,6,1,1] => 1
[7,5,3] => 0
[7,5,2,1] => 0
[7,5,1,1,1] => 2
[7,4,4] => 0
[7,4,3,1] => 0
[7,4,2,2] => 0
[7,4,2,1,1] => 2
[7,4,1,1,1,1] => 4
[7,3,3,2] => 0
[7,3,3,1,1] => 2
[7,3,2,2,1] => 3
[7,3,2,1,1,1] => 7
[7,3,1,1,1,1,1] => 7
[7,2,2,2,2] => 3
[7,2,2,2,1,1] => 8
[7,2,2,1,1,1,1] => 11
[7,2,1,1,1,1,1,1] => 11
[7,1,1,1,1,1,1,1,1] => 9
[6,6,3] => 0
[6,6,2,1] => 0
[6,6,1,1,1] => 2
[6,5,4] => 0
[6,5,3,1] => 0
[6,5,2,2] => 0
[6,5,2,1,1] => 2
[6,5,1,1,1,1] => 3
[6,4,4,1] => 0
[6,4,3,2] => 0
[6,4,3,1,1] => 1
[6,4,2,2,1] => 2
[6,4,2,1,1,1] => 5
[6,4,1,1,1,1,1] => 7
[6,3,3,3] => 0
[6,3,3,2,1] => 1
[6,3,3,1,1,1] => 5
[6,3,2,2,2] => 4
[6,3,2,2,1,1] => 9
[6,3,2,1,1,1,1] => 12
[6,3,1,1,1,1,1,1] => 12
[6,2,2,2,2,1] => 8
[6,2,2,2,1,1,1] => 15
[6,2,2,1,1,1,1,1] => 17
[6,2,1,1,1,1,1,1,1] => 17
[6,1,1,1,1,1,1,1,1,1] => 12
[5,5,5] => 0
[5,5,4,1] => 0
[5,5,3,2] => 0
[5,5,3,1,1] => 1
[5,5,2,2,1] => 1
[5,5,2,1,1,1] => 5
[5,5,1,1,1,1,1] => 7
[5,4,4,2] => 0
[5,4,4,1,1] => 1
[5,4,3,3] => 0
[5,4,3,2,1] => 0
[5,4,3,1,1,1] => 5
[5,4,2,2,2] => 4
[5,4,2,2,1,1] => 8
[5,4,2,1,1,1,1] => 13
[5,4,1,1,1,1,1,1] => 13
[5,3,3,3,1] => 3
[5,3,3,2,2] => 3
[5,3,3,2,1,1] => 8
[5,3,3,1,1,1,1] => 11
[5,3,2,2,2,1] => 12
[5,3,2,2,1,1,1] => 20
[5,3,2,1,1,1,1,1] => 23
[5,3,1,1,1,1,1,1,1] => 18
[5,2,2,2,2,2] => 6
[5,2,2,2,2,1,1] => 17
[5,2,2,2,1,1,1,1] => 24
[5,2,2,1,1,1,1,1,1] => 26
[5,2,1,1,1,1,1,1,1,1] => 23
[5,1,1,1,1,1,1,1,1,1,1] => 15
[4,4,4,3] => 0
[4,4,4,2,1] => 1
[4,4,4,1,1,1] => 5
[4,4,3,3,1] => 2
[4,4,3,2,2] => 3
[4,4,3,2,1,1] => 8
[4,4,3,1,1,1,1] => 13
[4,4,2,2,2,1] => 9
[4,4,2,2,1,1,1] => 17
[4,4,2,1,1,1,1,1] => 20
[4,4,1,1,1,1,1,1,1] => 15
[4,3,3,3,2] => 4
[4,3,3,3,1,1] => 8
[4,3,3,2,2,1] => 13
[4,3,3,2,1,1,1] => 22
[4,3,3,1,1,1,1,1] => 20
[4,3,2,2,2,2] => 10
[4,3,2,2,2,1,1] => 26
[4,3,2,2,1,1,1,1] => 37
[4,3,2,1,1,1,1,1,1] => 35
[4,3,1,1,1,1,1,1,1,1] => 24
[4,2,2,2,2,2,1] => 14
[4,2,2,2,2,1,1,1] => 27
[4,2,2,2,1,1,1,1,1] => 35
[4,2,2,1,1,1,1,1,1,1] => 35
[4,2,1,1,1,1,1,1,1,1,1] => 29
[4,1,1,1,1,1,1,1,1,1,1,1] => 18
[3,3,3,3,3] => 2
[3,3,3,3,2,1] => 8
[3,3,3,3,1,1,1] => 12
[3,3,3,2,2,2] => 8
[3,3,3,2,2,1,1] => 22
[3,3,3,2,1,1,1,1] => 27
[3,3,3,1,1,1,1,1,1] => 20
[3,3,2,2,2,2,1] => 18
[3,3,2,2,2,1,1,1] => 35
[3,3,2,2,1,1,1,1,1] => 41
[3,3,2,1,1,1,1,1,1,1] => 36
[3,3,1,1,1,1,1,1,1,1,1] => 23
[3,2,2,2,2,2,2] => 9
[3,2,2,2,2,2,1,1] => 26
[3,2,2,2,2,1,1,1,1] => 40
[3,2,2,2,1,1,1,1,1,1] => 46
[3,2,2,1,1,1,1,1,1,1,1] => 44
[3,2,1,1,1,1,1,1,1,1,1,1] => 35
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 21
[2,2,2,2,2,2,2,1] => 11
[2,2,2,2,2,2,1,1,1] => 23
[2,2,2,2,2,1,1,1,1,1] => 31
[2,2,2,2,1,1,1,1,1,1,1] => 35
[2,2,2,1,1,1,1,1,1,1,1,1] => 35
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 31
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 24
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 14
[16] => 0
[15,1] => 0
[14,2] => 0
[14,1,1] => 1
[13,3] => 0
[13,2,1] => 0
[13,1,1,1] => 2
[12,4] => 0
[12,3,1] => 0
[12,2,2] => 0
[12,2,1,1] => 2
[12,1,1,1,1] => 3
[11,5] => 0
[11,4,1] => 0
[11,3,2] => 0
[11,3,1,1] => 1
[11,2,2,1] => 1
[11,2,1,1,1] => 4
[11,1,1,1,1,1] => 4
[10,6] => 0
[10,5,1] => 0
[10,4,2] => 0
[10,4,1,1] => 1
[10,3,3] => 0
[10,3,2,1] => 0
[10,3,1,1,1] => 3
[10,2,2,2] => 1
[10,2,2,1,1] => 4
[10,2,1,1,1,1] => 6
[10,1,1,1,1,1,1] => 5
[9,7] => 0
[9,6,1] => 0
[9,5,2] => 0
[9,5,1,1] => 1
[9,4,3] => 0
[9,4,2,1] => 0
[9,4,1,1,1] => 2
[9,3,3,1] => 0
[9,3,2,2] => 1
[9,3,2,1,1] => 3
[9,3,1,1,1,1] => 5
[9,2,2,2,1] => 3
[9,2,2,1,1,1] => 7
[9,2,1,1,1,1,1] => 8
[9,1,1,1,1,1,1,1] => 6
[8,8] => 0
[8,7,1] => 0
[8,6,2] => 0
[8,6,1,1] => 1
[8,5,3] => 0
[8,5,2,1] => 0
[8,5,1,1,1] => 2
[8,4,4] => 0
[8,4,3,1] => 0
[8,4,2,2] => 0
[8,4,2,1,1] => 2
[8,4,1,1,1,1] => 4
[8,3,3,2] => 0
[8,3,3,1,1] => 2
[8,3,2,2,1] => 3
[8,3,2,1,1,1] => 7
[8,3,1,1,1,1,1] => 7
[8,2,2,2,2] => 2
[8,2,2,2,1,1] => 7
[8,2,2,1,1,1,1] => 10
[8,2,1,1,1,1,1,1] => 10
[8,1,1,1,1,1,1,1,1] => 8
[7,7,2] => 0
[7,7,1,1] => 1
[7,6,3] => 0
[7,6,2,1] => 0
[7,6,1,1,1] => 2
[7,5,4] => 0
[7,5,3,1] => 0
[7,5,2,2] => 0
[7,5,2,1,1] => 2
[7,5,1,1,1,1] => 3
[7,4,4,1] => 0
[7,4,3,2] => 0
[7,4,3,1,1] => 1
[7,4,2,2,1] => 2
[7,4,2,1,1,1] => 5
[7,4,1,1,1,1,1] => 6
[7,3,3,3] => 0
[7,3,3,2,1] => 1
[7,3,3,1,1,1] => 5
[7,3,2,2,2] => 3
[7,3,2,2,1,1] => 8
[7,3,2,1,1,1,1] => 11
[7,3,1,1,1,1,1,1] => 10
[7,2,2,2,2,1] => 7
[7,2,2,2,1,1,1] => 13
[7,2,2,1,1,1,1,1] => 15
[7,2,1,1,1,1,1,1,1] => 15
[7,1,1,1,1,1,1,1,1,1] => 11
[6,6,4] => 0
[6,6,3,1] => 0
[6,6,2,2] => 0
[6,6,2,1,1] => 2
[6,6,1,1,1,1] => 3
[6,5,5] => 0
[6,5,4,1] => 0
[6,5,3,2] => 0
[6,5,3,1,1] => 1
[6,5,2,2,1] => 1
[6,5,2,1,1,1] => 4
[6,5,1,1,1,1,1] => 6
[6,4,4,2] => 0
[6,4,4,1,1] => 1
[6,4,3,3] => 0
[6,4,3,2,1] => 0
[6,4,3,1,1,1] => 4
[6,4,2,2,2] => 2
[6,4,2,2,1,1] => 6
[6,4,2,1,1,1,1] => 10
[6,4,1,1,1,1,1,1] => 11
[6,3,3,3,1] => 2
[6,3,3,2,2] => 3
[6,3,3,2,1,1] => 7
[6,3,3,1,1,1,1] => 9
[6,3,2,2,2,1] => 10
[6,3,2,2,1,1,1] => 17
[6,3,2,1,1,1,1,1] => 19
[6,3,1,1,1,1,1,1,1] => 16
[6,2,2,2,2,2] => 5
[6,2,2,2,2,1,1] => 15
[6,2,2,2,1,1,1,1] => 21
[6,2,2,1,1,1,1,1,1] => 23
[6,2,1,1,1,1,1,1,1,1] => 21
[6,1,1,1,1,1,1,1,1,1,1] => 14
[5,5,5,1] => 0
[5,5,4,2] => 0
[5,5,4,1,1] => 1
[5,5,3,3] => 0
[5,5,3,2,1] => 0
[5,5,3,1,1,1] => 4
[5,5,2,2,2] => 2
[5,5,2,2,1,1] => 6
[5,5,2,1,1,1,1] => 10
[5,5,1,1,1,1,1,1] => 10
[5,4,4,3] => 0
[5,4,4,2,1] => 0
[5,4,4,1,1,1] => 4
[5,4,3,3,1] => 1
[5,4,3,2,2] => 3
[5,4,3,2,1,1] => 5
[5,4,3,1,1,1,1] => 12
[5,4,2,2,2,1] => 10
[5,4,2,2,1,1,1] => 16
[5,4,2,1,1,1,1,1] => 21
[5,4,1,1,1,1,1,1,1] => 17
[5,3,3,3,2] => 3
[5,3,3,3,1,1] => 7
[5,3,3,2,2,1] => 10
[5,3,3,2,1,1,1] => 17
[5,3,3,1,1,1,1,1] => 17
[5,3,2,2,2,2] => 9
[5,3,2,2,2,1,1] => 23
[5,3,2,2,1,1,1,1] => 31
[5,3,2,1,1,1,1,1,1] => 31
[5,3,1,1,1,1,1,1,1,1] => 22
[5,2,2,2,2,2,1] => 13
[5,2,2,2,2,1,1,1] => 25
[5,2,2,2,1,1,1,1,1] => 32
[5,2,2,1,1,1,1,1,1,1] => 32
[5,2,1,1,1,1,1,1,1,1,1] => 27
[5,1,1,1,1,1,1,1,1,1,1,1] => 17
[4,4,4,4] => 0
[4,4,4,3,1] => 1
[4,4,4,2,2] => 1
[4,4,4,2,1,1] => 6
[4,4,4,1,1,1,1] => 9
[4,4,3,3,2] => 3
[4,4,3,3,1,1] => 7
[4,4,3,2,2,1] => 10
[4,4,3,2,1,1,1] => 19
[4,4,3,1,1,1,1,1] => 19
[4,4,2,2,2,2] => 6
[4,4,2,2,2,1,1] => 18
[4,4,2,2,1,1,1,1] => 26
[4,4,2,1,1,1,1,1,1] => 26
[4,4,1,1,1,1,1,1,1,1] => 18
[4,3,3,3,3] => 3
[4,3,3,3,2,1] => 10
[4,3,3,3,1,1,1] => 15
[4,3,3,2,2,2] => 11
[4,3,3,2,2,1,1] => 27
[4,3,3,2,1,1,1,1] => 34
[4,3,3,1,1,1,1,1,1] => 26
[4,3,2,2,2,2,1] => 22
[4,3,2,2,2,1,1,1] => 41
[4,3,2,2,1,1,1,1,1] => 49
[4,3,2,1,1,1,1,1,1,1] => 43
[4,3,1,1,1,1,1,1,1,1,1] => 28
[4,2,2,2,2,2,2] => 8
[4,2,2,2,2,2,1,1] => 24
[4,2,2,2,2,1,1,1,1] => 37
[4,2,2,2,1,1,1,1,1,1] => 43
[4,2,2,1,1,1,1,1,1,1,1] => 41
[4,2,1,1,1,1,1,1,1,1,1,1] => 33
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 20
[3,3,3,3,3,1] => 5
[3,3,3,3,2,2] => 7
[3,3,3,3,2,1,1] => 17
[3,3,3,3,1,1,1,1] => 17
[3,3,3,2,2,2,1] => 19
[3,3,3,2,2,1,1,1] => 34
[3,3,3,2,1,1,1,1,1] => 35
[3,3,3,1,1,1,1,1,1,1] => 24
[3,3,2,2,2,2,2] => 11
[3,3,2,2,2,2,1,1] => 32
[3,3,2,2,2,1,1,1,1] => 47
[3,3,2,2,1,1,1,1,1,1] => 50
[3,3,2,1,1,1,1,1,1,1,1] => 42
[3,3,1,1,1,1,1,1,1,1,1,1] => 26
[3,2,2,2,2,2,2,1] => 19
[3,2,2,2,2,2,1,1,1] => 38
[3,2,2,2,2,1,1,1,1,1] => 50
[3,2,2,2,1,1,1,1,1,1,1] => 54
[3,2,2,1,1,1,1,1,1,1,1,1] => 50
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 39
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 23
[2,2,2,2,2,2,2,2] => 6
[2,2,2,2,2,2,2,1,1] => 19
[2,2,2,2,2,2,1,1,1,1] => 30
[2,2,2,2,2,1,1,1,1,1,1] => 37
[2,2,2,2,1,1,1,1,1,1,1,1] => 40
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 39
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 34
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 26
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 15
[17] => 0
[16,1] => 0
[15,2] => 0
[15,1,1] => 1
[14,3] => 0
[14,2,1] => 0
[14,1,1,1] => 2
[13,4] => 0
[13,3,1] => 0
[13,2,2] => 0
[13,2,1,1] => 2
[13,1,1,1,1] => 3
[12,5] => 0
[12,4,1] => 0
[12,3,2] => 0
[12,3,1,1] => 1
[12,2,2,1] => 1
[12,2,1,1,1] => 4
[12,1,1,1,1,1] => 4
[11,6] => 0
[11,5,1] => 0
[11,4,2] => 0
[11,4,1,1] => 1
[11,3,3] => 0
[11,3,2,1] => 0
[11,3,1,1,1] => 3
[11,2,2,2] => 1
[11,2,2,1,1] => 4
[11,2,1,1,1,1] => 6
[11,1,1,1,1,1,1] => 5
[10,7] => 0
[10,6,1] => 0
[10,5,2] => 0
[10,5,1,1] => 1
[10,4,3] => 0
[10,4,2,1] => 0
[10,4,1,1,1] => 2
[10,3,3,1] => 0
[10,3,2,2] => 1
[10,3,2,1,1] => 3
[10,3,1,1,1,1] => 5
[10,2,2,2,1] => 3
[10,2,2,1,1,1] => 7
[10,2,1,1,1,1,1] => 8
[10,1,1,1,1,1,1,1] => 6
[9,8] => 0
[9,7,1] => 0
[9,6,2] => 0
[9,6,1,1] => 1
[9,5,3] => 0
[9,5,2,1] => 0
[9,5,1,1,1] => 2
[9,4,4] => 0
[9,4,3,1] => 0
[9,4,2,2] => 0
[9,4,2,1,1] => 2
[9,4,1,1,1,1] => 4
[9,3,3,2] => 0
[9,3,3,1,1] => 2
[9,3,2,2,1] => 3
[9,3,2,1,1,1] => 7
[9,3,1,1,1,1,1] => 7
[9,2,2,2,2] => 2
[9,2,2,2,1,1] => 7
[9,2,2,1,1,1,1] => 10
[9,2,1,1,1,1,1,1] => 10
[9,1,1,1,1,1,1,1,1] => 7
[8,8,1] => 0
[8,7,2] => 0
[8,7,1,1] => 1
[8,6,3] => 0
[8,6,2,1] => 0
[8,6,1,1,1] => 2
[8,5,4] => 0
[8,5,3,1] => 0
[8,5,2,2] => 0
[8,5,2,1,1] => 2
[8,5,1,1,1,1] => 3
[8,4,4,1] => 0
[8,4,3,2] => 0
[8,4,3,1,1] => 1
[8,4,2,2,1] => 2
[8,4,2,1,1,1] => 5
[8,4,1,1,1,1,1] => 6
[8,3,3,3] => 0
[8,3,3,2,1] => 1
[8,3,3,1,1,1] => 5
[8,3,2,2,2] => 3
[8,3,2,2,1,1] => 8
[8,3,2,1,1,1,1] => 11
[8,3,1,1,1,1,1,1] => 9
[8,2,2,2,2,1] => 6
[8,2,2,2,1,1,1] => 12
[8,2,2,1,1,1,1,1] => 14
[8,2,1,1,1,1,1,1,1] => 13
[8,1,1,1,1,1,1,1,1,1] => 10
[7,7,3] => 0
[7,7,2,1] => 0
[7,7,1,1,1] => 2
[7,6,4] => 0
[7,6,3,1] => 0
[7,6,2,2] => 0
[7,6,2,1,1] => 2
[7,6,1,1,1,1] => 3
[7,5,5] => 0
[7,5,4,1] => 0
[7,5,3,2] => 0
[7,5,3,1,1] => 1
[7,5,2,2,1] => 1
[7,5,2,1,1,1] => 4
[7,5,1,1,1,1,1] => 5
[7,4,4,2] => 0
[7,4,4,1,1] => 1
[7,4,3,3] => 0
[7,4,3,2,1] => 0
[7,4,3,1,1,1] => 4
[7,4,2,2,2] => 2
[7,4,2,2,1,1] => 6
[7,4,2,1,1,1,1] => 9
[7,4,1,1,1,1,1,1] => 9
[7,3,3,3,1] => 1
[7,3,3,2,2] => 2
[7,3,3,2,1,1] => 6
[7,3,3,1,1,1,1] => 8
[7,3,2,2,2,1] => 8
[7,3,2,2,1,1,1] => 15
[7,3,2,1,1,1,1,1] => 16
[7,3,1,1,1,1,1,1,1] => 14
[7,2,2,2,2,2] => 5
[7,2,2,2,2,1,1] => 14
[7,2,2,2,1,1,1,1] => 19
[7,2,2,1,1,1,1,1,1] => 20
[7,2,1,1,1,1,1,1,1,1] => 19
[7,1,1,1,1,1,1,1,1,1,1] => 13
[6,6,5] => 0
[6,6,4,1] => 0
[6,6,3,2] => 0
[6,6,3,1,1] => 1
[6,6,2,2,1] => 1
[6,6,2,1,1,1] => 4
[6,6,1,1,1,1,1] => 5
[6,5,5,1] => 0
[6,5,4,2] => 0
[6,5,4,1,1] => 1
[6,5,3,3] => 0
[6,5,3,2,1] => 0
[6,5,3,1,1,1] => 3
[6,5,2,2,2] => 2
[6,5,2,2,1,1] => 5
[6,5,2,1,1,1,1] => 8
[6,5,1,1,1,1,1,1] => 10
[6,4,4,3] => 0
[6,4,4,2,1] => 0
[6,4,4,1,1,1] => 3
[6,4,3,3,1] => 0
[6,4,3,2,2] => 2
[6,4,3,2,1,1] => 4
[6,4,3,1,1,1,1] => 9
[6,4,2,2,2,1] => 8
[6,4,2,2,1,1,1] => 13
[6,4,2,1,1,1,1,1] => 17
[6,4,1,1,1,1,1,1,1] => 15
[6,3,3,3,2] => 2
[6,3,3,3,1,1] => 6
[6,3,3,2,2,1] => 8
[6,3,3,2,1,1,1] => 14
[6,3,3,1,1,1,1,1] => 14
[6,3,2,2,2,2] => 8
[6,3,2,2,2,1,1] => 20
[6,3,2,2,1,1,1,1] => 26
[6,3,2,1,1,1,1,1,1] => 27
[6,3,1,1,1,1,1,1,1,1] => 20
[6,2,2,2,2,2,1] => 12
[6,2,2,2,2,1,1,1] => 23
[6,2,2,2,1,1,1,1,1] => 28
[6,2,2,1,1,1,1,1,1,1] => 29
[6,2,1,1,1,1,1,1,1,1,1] => 25
[6,1,1,1,1,1,1,1,1,1,1,1] => 16
[5,5,5,2] => 0
[5,5,5,1,1] => 1
[5,5,4,3] => 0
[5,5,4,2,1] => 0
[5,5,4,1,1,1] => 3
[5,5,3,3,1] => 0
[5,5,3,2,2] => 1
[5,5,3,2,1,1] => 4
[5,5,3,1,1,1,1] => 9
[5,5,2,2,2,1] => 6
[5,5,2,2,1,1,1] => 12
[5,5,2,1,1,1,1,1] => 16
[5,5,1,1,1,1,1,1,1] => 13
[5,4,4,4] => 0
[5,4,4,3,1] => 0
[5,4,4,2,2] => 1
[5,4,4,2,1,1] => 4
[5,4,4,1,1,1,1] => 9
[5,4,3,3,2] => 2
[5,4,3,3,1,1] => 5
[5,4,3,2,2,1] => 9
[5,4,3,2,1,1,1] => 16
[5,4,3,1,1,1,1,1] => 20
[5,4,2,2,2,2] => 8
[5,4,2,2,2,1,1] => 20
[5,4,2,2,1,1,1,1] => 27
[5,4,2,1,1,1,1,1,1] => 29
[5,4,1,1,1,1,1,1,1,1] => 21
[5,3,3,3,3] => 3
[5,3,3,3,2,1] => 9
[5,3,3,3,1,1,1] => 13
[5,3,3,2,2,2] => 9
[5,3,3,2,2,1,1] => 22
[5,3,3,2,1,1,1,1] => 28
[5,3,3,1,1,1,1,1,1] => 23
[5,3,2,2,2,2,1] => 20
[5,3,2,2,2,1,1,1] => 36
[5,3,2,2,1,1,1,1,1] => 43
[5,3,2,1,1,1,1,1,1,1] => 39
[5,3,1,1,1,1,1,1,1,1,1] => 26
[5,2,2,2,2,2,2] => 8
[5,2,2,2,2,2,1,1] => 23
[5,2,2,2,2,1,1,1,1] => 34
[5,2,2,2,1,1,1,1,1,1] => 40
[5,2,2,1,1,1,1,1,1,1,1] => 38
[5,2,1,1,1,1,1,1,1,1,1,1] => 31
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 19
[4,4,4,4,1] => 1
[4,4,4,3,2] => 1
[4,4,4,3,1,1] => 5
[4,4,4,2,2,1] => 6
[4,4,4,2,1,1,1] => 13
[4,4,4,1,1,1,1,1] => 13
[4,4,3,3,3] => 3
[4,4,3,3,2,1] => 8
[4,4,3,3,1,1,1] => 15
[4,4,3,2,2,2] => 9
[4,4,3,2,2,1,1] => 23
[4,4,3,2,1,1,1,1] => 31
[4,4,3,1,1,1,1,1,1] => 25
[4,4,2,2,2,2,1] => 15
[4,4,2,2,2,1,1,1] => 29
[4,4,2,2,1,1,1,1,1] => 35
[4,4,2,1,1,1,1,1,1,1] => 32
[4,4,1,1,1,1,1,1,1,1,1] => 21
[4,3,3,3,3,1] => 7
[4,3,3,3,2,2] => 10
[4,3,3,3,2,1,1] => 22
[4,3,3,3,1,1,1,1] => 23
[4,3,3,2,2,2,1] => 25
[4,3,3,2,2,1,1,1] => 44
[4,3,3,2,1,1,1,1,1] => 46
[4,3,3,1,1,1,1,1,1,1] => 32
[4,3,2,2,2,2,2] => 14
[4,3,2,2,2,2,1,1] => 38
[4,3,2,2,2,1,1,1,1] => 57
[4,3,2,2,1,1,1,1,1,1] => 61
[4,3,2,1,1,1,1,1,1,1,1] => 51
[4,3,1,1,1,1,1,1,1,1,1,1] => 32
[4,2,2,2,2,2,2,1] => 18
[4,2,2,2,2,2,1,1,1] => 35
[4,2,2,2,2,1,1,1,1,1] => 47
[4,2,2,2,1,1,1,1,1,1,1] => 51
[4,2,2,1,1,1,1,1,1,1,1,1] => 47
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 37
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 22
[3,3,3,3,3,2] => 5
[3,3,3,3,3,1,1] => 10
[3,3,3,3,2,2,1] => 17
[3,3,3,3,2,1,1,1] => 27
[3,3,3,3,1,1,1,1,1] => 22
[3,3,3,2,2,2,2] => 12
[3,3,3,2,2,2,1,1] => 34
[3,3,3,2,2,1,1,1,1] => 46
[3,3,3,2,1,1,1,1,1,1] => 43
[3,3,3,1,1,1,1,1,1,1,1] => 28
[3,3,2,2,2,2,2,1] => 24
[3,3,2,2,2,2,1,1,1] => 47
[3,3,2,2,2,1,1,1,1,1] => 59
[3,3,2,2,1,1,1,1,1,1,1] => 59
[3,3,2,1,1,1,1,1,1,1,1,1] => 48
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 29
[3,2,2,2,2,2,2,2] => 11
[3,2,2,2,2,2,2,1,1] => 32
[3,2,2,2,2,2,1,1,1,1] => 50
[3,2,2,2,2,1,1,1,1,1,1] => 60
[3,2,2,2,1,1,1,1,1,1,1,1] => 62
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 56
-----------------------------------------------------------------------------
Created: Apr 23, 2021 at 09:54 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Apr 23, 2021 at 09:54 by Martin Rubey