*****************************************************************************
* 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: St000992
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The alternating sum of the parts of an integer partition.
For a partition $\lambda = (\lambda_1,\ldots,\lambda_k)$, this is $\lambda_1 - \lambda_2 + \cdots \pm \lambda_k$.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(L):
return sum((-1)^k*p for k, p in enumerate(L))
-----------------------------------------------------------------------------
Statistic values:
[] => 0
[1] => 1
[2] => 2
[1,1] => 0
[3] => 3
[2,1] => 1
[1,1,1] => 1
[4] => 4
[3,1] => 2
[2,2] => 0
[2,1,1] => 2
[1,1,1,1] => 0
[5] => 5
[4,1] => 3
[3,2] => 1
[3,1,1] => 3
[2,2,1] => 1
[2,1,1,1] => 1
[1,1,1,1,1] => 1
[6] => 6
[5,1] => 4
[4,2] => 2
[4,1,1] => 4
[3,3] => 0
[3,2,1] => 2
[3,1,1,1] => 2
[2,2,2] => 2
[2,2,1,1] => 0
[2,1,1,1,1] => 2
[1,1,1,1,1,1] => 0
[7] => 7
[6,1] => 5
[5,2] => 3
[5,1,1] => 5
[4,3] => 1
[4,2,1] => 3
[4,1,1,1] => 3
[3,3,1] => 1
[3,2,2] => 3
[3,2,1,1] => 1
[3,1,1,1,1] => 3
[2,2,2,1] => 1
[2,2,1,1,1] => 1
[2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1] => 1
[8] => 8
[7,1] => 6
[6,2] => 4
[6,1,1] => 6
[5,3] => 2
[5,2,1] => 4
[5,1,1,1] => 4
[4,4] => 0
[4,3,1] => 2
[4,2,2] => 4
[4,2,1,1] => 2
[4,1,1,1,1] => 4
[3,3,2] => 2
[3,3,1,1] => 0
[3,2,2,1] => 2
[3,2,1,1,1] => 2
[3,1,1,1,1,1] => 2
[2,2,2,2] => 0
[2,2,2,1,1] => 2
[2,2,1,1,1,1] => 0
[2,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1] => 0
[9] => 9
[8,1] => 7
[7,2] => 5
[7,1,1] => 7
[6,3] => 3
[6,2,1] => 5
[6,1,1,1] => 5
[5,4] => 1
[5,3,1] => 3
[5,2,2] => 5
[5,2,1,1] => 3
[5,1,1,1,1] => 5
[4,4,1] => 1
[4,3,2] => 3
[4,3,1,1] => 1
[4,2,2,1] => 3
[4,2,1,1,1] => 3
[4,1,1,1,1,1] => 3
[3,3,3] => 3
[3,3,2,1] => 1
[3,3,1,1,1] => 1
[3,2,2,2] => 1
[3,2,2,1,1] => 3
[3,2,1,1,1,1] => 1
[3,1,1,1,1,1,1] => 3
[2,2,2,2,1] => 1
[2,2,2,1,1,1] => 1
[2,2,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1] => 1
[10] => 10
[9,1] => 8
[8,2] => 6
[8,1,1] => 8
[7,3] => 4
[7,2,1] => 6
[7,1,1,1] => 6
[6,4] => 2
[6,3,1] => 4
[6,2,2] => 6
[6,2,1,1] => 4
[6,1,1,1,1] => 6
[5,5] => 0
[5,4,1] => 2
[5,3,2] => 4
[5,3,1,1] => 2
[5,2,2,1] => 4
[5,2,1,1,1] => 4
[5,1,1,1,1,1] => 4
[4,4,2] => 2
[4,4,1,1] => 0
[4,3,3] => 4
[4,3,2,1] => 2
[4,3,1,1,1] => 2
[4,2,2,2] => 2
[4,2,2,1,1] => 4
[4,2,1,1,1,1] => 2
[4,1,1,1,1,1,1] => 4
[3,3,3,1] => 2
[3,3,2,2] => 0
[3,3,2,1,1] => 2
[3,3,1,1,1,1] => 0
[3,2,2,2,1] => 2
[3,2,2,1,1,1] => 2
[3,2,1,1,1,1,1] => 2
[3,1,1,1,1,1,1,1] => 2
[2,2,2,2,2] => 2
[2,2,2,2,1,1] => 0
[2,2,2,1,1,1,1] => 2
[2,2,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1] => 0
[11] => 11
[10,1] => 9
[9,2] => 7
[9,1,1] => 9
[8,3] => 5
[8,2,1] => 7
[8,1,1,1] => 7
[7,4] => 3
[7,3,1] => 5
[7,2,2] => 7
[7,2,1,1] => 5
[7,1,1,1,1] => 7
[6,5] => 1
[6,4,1] => 3
[6,3,2] => 5
[6,3,1,1] => 3
[6,2,2,1] => 5
[6,2,1,1,1] => 5
[6,1,1,1,1,1] => 5
[5,5,1] => 1
[5,4,2] => 3
[5,4,1,1] => 1
[5,3,3] => 5
[5,3,2,1] => 3
[5,3,1,1,1] => 3
[5,2,2,2] => 3
[5,2,2,1,1] => 5
[5,2,1,1,1,1] => 3
[5,1,1,1,1,1,1] => 5
[4,4,3] => 3
[4,4,2,1] => 1
[4,4,1,1,1] => 1
[4,3,3,1] => 3
[4,3,2,2] => 1
[4,3,2,1,1] => 3
[4,3,1,1,1,1] => 1
[4,2,2,2,1] => 3
[4,2,2,1,1,1] => 3
[4,2,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1] => 3
[3,3,3,2] => 1
[3,3,3,1,1] => 3
[3,3,2,2,1] => 1
[3,3,2,1,1,1] => 1
[3,3,1,1,1,1,1] => 1
[3,2,2,2,2] => 3
[3,2,2,2,1,1] => 1
[3,2,2,1,1,1,1] => 3
[3,2,1,1,1,1,1,1] => 1
[3,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,1] => 1
[2,2,2,2,1,1,1] => 1
[2,2,2,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1] => 1
[12] => 12
[11,1] => 10
[10,2] => 8
[10,1,1] => 10
[9,3] => 6
[9,2,1] => 8
[9,1,1,1] => 8
[8,4] => 4
[8,3,1] => 6
[8,2,2] => 8
[8,2,1,1] => 6
[8,1,1,1,1] => 8
[7,5] => 2
[7,4,1] => 4
[7,3,2] => 6
[7,3,1,1] => 4
[7,2,2,1] => 6
[7,2,1,1,1] => 6
[7,1,1,1,1,1] => 6
[6,6] => 0
[6,5,1] => 2
[6,4,2] => 4
[6,4,1,1] => 2
[6,3,3] => 6
[6,3,2,1] => 4
[6,3,1,1,1] => 4
[6,2,2,2] => 4
[6,2,2,1,1] => 6
[6,2,1,1,1,1] => 4
[6,1,1,1,1,1,1] => 6
[5,5,2] => 2
[5,5,1,1] => 0
[5,4,3] => 4
[5,4,2,1] => 2
[5,4,1,1,1] => 2
[5,3,3,1] => 4
[5,3,2,2] => 2
[5,3,2,1,1] => 4
[5,3,1,1,1,1] => 2
[5,2,2,2,1] => 4
[5,2,2,1,1,1] => 4
[5,2,1,1,1,1,1] => 4
[5,1,1,1,1,1,1,1] => 4
[4,4,4] => 4
[4,4,3,1] => 2
[4,4,2,2] => 0
[4,4,2,1,1] => 2
[4,4,1,1,1,1] => 0
[4,3,3,2] => 2
[4,3,3,1,1] => 4
[4,3,2,2,1] => 2
[4,3,2,1,1,1] => 2
[4,3,1,1,1,1,1] => 2
[4,2,2,2,2] => 4
[4,2,2,2,1,1] => 2
[4,2,2,1,1,1,1] => 4
[4,2,1,1,1,1,1,1] => 2
[4,1,1,1,1,1,1,1,1] => 4
[3,3,3,3] => 0
[3,3,3,2,1] => 2
[3,3,3,1,1,1] => 2
[3,3,2,2,2] => 2
[3,3,2,2,1,1] => 0
[3,3,2,1,1,1,1] => 2
[3,3,1,1,1,1,1,1] => 0
[3,2,2,2,2,1] => 2
[3,2,2,2,1,1,1] => 2
[3,2,2,1,1,1,1,1] => 2
[3,2,1,1,1,1,1,1,1] => 2
[3,1,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,2] => 0
[2,2,2,2,2,1,1] => 2
[2,2,2,2,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1] => 2
[2,2,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[13] => 13
[12,1] => 11
[10,3] => 7
[9,4] => 5
[9,2,2] => 9
[9,2,1,1] => 7
[8,5] => 3
[8,4,1] => 5
[8,3,2] => 7
[8,3,1,1] => 5
[7,6] => 1
[7,5,1] => 3
[7,4,2] => 5
[7,4,1,1] => 3
[7,3,3] => 7
[7,3,2,1] => 5
[7,2,2,2] => 5
[7,2,1,1,1,1] => 5
[7,1,1,1,1,1,1] => 7
[6,6,1] => 1
[6,5,2] => 3
[6,5,1,1] => 1
[6,4,3] => 5
[6,4,2,1] => 3
[6,3,3,1] => 5
[6,3,2,2] => 3
[6,3,1,1,1,1] => 3
[6,2,2,2,1] => 5
[6,2,2,1,1,1] => 5
[6,1,1,1,1,1,1,1] => 5
[5,5,3] => 3
[5,5,2,1] => 1
[5,4,4] => 5
[5,4,3,1] => 3
[5,4,2,2] => 1
[5,4,2,1,1] => 3
[5,4,1,1,1,1] => 1
[5,3,3,2] => 3
[5,3,3,1,1] => 5
[5,3,2,2,1] => 3
[5,3,2,1,1,1] => 3
[5,3,1,1,1,1,1] => 3
[5,2,2,2,1,1] => 3
[5,2,2,1,1,1,1] => 5
[5,2,1,1,1,1,1,1] => 3
[4,4,4,1] => 3
[4,4,3,2] => 1
[4,4,3,1,1] => 3
[4,4,2,2,1] => 1
[4,3,3,3] => 1
[4,3,3,2,1] => 3
[4,2,2,2,2,1] => 3
[3,3,3,3,1] => 1
[3,3,3,2,2] => 3
[3,3,3,2,1,1] => 1
[3,3,2,2,2,1] => 1
[3,3,2,2,1,1,1] => 1
[3,3,2,1,1,1,1,1] => 1
[3,3,1,1,1,1,1,1,1] => 1
[3,2,2,2,2,2] => 1
[3,2,2,2,2,1,1] => 3
[3,2,2,1,1,1,1,1,1] => 3
[3,2,1,1,1,1,1,1,1,1] => 1
[3,1,1,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,2,1] => 1
[2,2,2,2,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[14] => 14
[13,1] => 12
[12,2] => 10
[12,1,1] => 12
[11,2,1] => 10
[11,1,1,1] => 10
[10,2,2] => 10
[9,5] => 4
[9,4,1] => 6
[9,2,2,1] => 8
[8,6] => 2
[8,5,1] => 4
[8,4,2] => 6
[8,3,3] => 8
[8,3,1,1,1] => 6
[8,1,1,1,1,1,1] => 8
[7,7] => 0
[7,6,1] => 2
[7,5,2] => 4
[7,4,3] => 6
[7,2,2,2,1] => 6
[6,6,2] => 2
[6,6,1,1] => 0
[6,5,3] => 4
[6,5,1,1,1] => 2
[6,4,4] => 6
[6,4,2,2] => 2
[6,2,2,2,2] => 6
[6,1,1,1,1,1,1,1,1] => 6
[5,5,4] => 4
[5,5,1,1,1,1] => 0
[5,4,4,1] => 4
[5,4,3,2] => 2
[5,4,3,1,1] => 4
[5,4,2,2,1] => 2
[5,4,2,1,1,1] => 2
[5,4,1,1,1,1,1] => 2
[5,3,3,3] => 2
[5,3,3,2,1] => 4
[5,3,2,2,2] => 4
[5,3,2,2,1,1] => 2
[5,3,2,1,1,1,1] => 4
[5,3,1,1,1,1,1,1] => 2
[5,2,2,2,2,1] => 4
[5,2,2,1,1,1,1,1] => 4
[4,4,4,2] => 2
[4,4,4,1,1] => 4
[4,4,3,3] => 0
[4,4,3,2,1] => 2
[4,3,2,2,2,1] => 2
[3,3,3,3,2] => 2
[3,3,3,3,1,1] => 0
[3,3,3,2,2,1] => 2
[3,3,2,2,2,2] => 0
[3,3,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,1,1,1] => 2
[2,2,2,2,2,2,2] => 2
[2,2,2,2,1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1] => 2
[2,2,1,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[15] => 15
[14,1] => 13
[12,3] => 9
[11,2,2] => 11
[9,6] => 3
[9,5,1] => 5
[9,3,2,1] => 7
[8,7] => 1
[8,5,2] => 5
[7,5,3] => 5
[6,6,3] => 3
[6,5,4] => 5
[6,5,1,1,1,1] => 1
[6,4,3,1,1] => 5
[6,3,3,3] => 3
[6,3,1,1,1,1,1,1] => 3
[6,2,2,2,2,1] => 5
[5,5,5] => 5
[5,5,2,2,1] => 1
[5,4,3,3] => 1
[5,4,3,2,1] => 3
[5,4,3,1,1,1] => 3
[5,3,2,2,2,1] => 3
[5,3,2,2,1,1,1] => 3
[5,3,1,1,1,1,1,1,1] => 3
[4,4,4,3] => 1
[4,4,4,1,1,1] => 3
[4,3,3,3,2] => 3
[3,3,3,3,3] => 3
[3,3,3,3,2,1] => 1
[3,3,3,2,2,2] => 1
[2,2,2,2,2,2,2,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[16] => 16
[15,1] => 14
[12,4] => 8
[12,1,1,1,1] => 12
[10,6] => 4
[9,1,1,1,1,1,1,1] => 8
[8,8] => 0
[8,6,2] => 4
[8,5,3] => 6
[7,6,3] => 4
[7,5,3,1] => 4
[7,5,1,1,1,1] => 2
[7,3,3,2,1] => 6
[6,6,4] => 4
[6,6,2,2] => 0
[6,5,5] => 6
[6,4,3,3] => 2
[5,5,3,3] => 0
[5,5,2,2,2] => 2
[5,4,4,3] => 2
[5,4,3,2,1,1] => 2
[5,4,2,2,2,1] => 2
[4,4,4,4] => 0
[4,4,4,2,2] => 4
[4,4,3,3,2] => 2
[4,4,2,2,2,2] => 0
[4,3,3,3,3] => 4
[4,3,3,3,2,1] => 2
[3,3,3,3,3,1] => 2
[3,3,3,3,2,2] => 0
[3,3,3,3,1,1,1,1] => 0
[3,3,2,2,2,2,2] => 2
[2,2,2,2,2,2,2,2] => 0
[2,2,2,2,2,2,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[17] => 17
[16,1] => 15
[9,8] => 1
[8,8,1] => 1
[8,6,3] => 5
[7,6,1,1,1,1] => 1
[7,5,3,2] => 3
[6,5,3,3] => 1
[6,5,2,2,2] => 3
[6,4,4,3] => 3
[6,4,4,1,1,1] => 5
[6,3,3,3,2] => 5
[6,3,3,3,1,1] => 3
[5,5,4,3] => 1
[5,5,4,1,1,1] => 3
[5,5,2,2,2,1] => 1
[5,4,4,4] => 1
[5,4,3,2,2,1] => 3
[5,3,3,3,2,1] => 3
[4,4,4,3,2] => 3
[4,4,4,3,1,1] => 1
[4,4,4,2,2,1] => 3
[4,4,3,3,3] => 3
[3,3,3,3,3,2] => 1
[3,2,2,2,2,2,2,2] => 1
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 3
[4,4,4,3,2,1] => 2
[5,4,3,3,2,1] => 2
[6,3,3,3,2,1] => 4
[6,5,2,2,2,1] => 2
[5,5,3,3,1,1] => 0
[6,5,4,1,1,1] => 4
[5,5,3,3,2] => 2
[5,5,4,2,2] => 4
[6,4,4,2,2] => 6
[6,5,4,3] => 2
[3,3,3,3,3,2,1] => 2
[4,4,4,3,3] => 4
[4,4,4,4,2] => 2
[5,5,4,4] => 0
[6,4,4,4] => 2
[7,6,5] => 6
[2,2,2,2,2,2,2,2,2] => 2
[3,3,3,3,3,3] => 0
[18] => 18
[6,2,2,2,2,2,2] => 6
[6,6,6] => 6
[4,2,2,2,2,2,2,2] => 2
[10,4,4] => 10
[9,6,3] => 6
[8,6,4] => 6
[10,8] => 2
[3,3,3,3,1,1,1,1,1,1] => 0
[9,9] => 0
[7,7,1,1,1,1] => 0
[9,1,1,1,1,1,1,1,1,1] => 8
[7,7,4] => 4
[5,4,4,3,2,1] => 3
[5,5,3,3,2,1] => 1
[5,5,4,2,2,1] => 3
[6,4,4,2,2,1] => 5
[5,5,4,3,1,1] => 1
[6,4,4,3,1,1] => 3
[6,5,3,3,1,1] => 1
[5,5,4,3,2] => 3
[6,4,4,3,2] => 5
[6,5,3,3,2] => 3
[6,5,4,2,2] => 5
[6,5,4,3,1] => 3
[6,5,4,1,1,1,1] => 5
[4,4,4,4,3] => 3
[4,3,3,3,3,3] => 1
[19] => 19
[7,2,2,2,2,2,2] => 7
[7,6,6] => 7
[5,2,2,2,2,2,2,2] => 3
[13,6] => 7
[11,4,4] => 11
[9,6,4] => 7
[8,5,4,2] => 5
[8,5,5,1] => 7
[5,5,4,3,2,1] => 2
[6,4,4,3,2,1] => 4
[6,5,3,3,2,1] => 2
[6,5,4,2,2,1] => 4
[6,5,4,3,1,1] => 2
[6,5,4,3,2] => 4
[6,5,2,2,2,2,1] => 2
[6,5,4,2,1,1,1] => 4
[6,6,2,2,2,2] => 0
[7,5,4,3,1] => 4
[2,2,2,2,2,2,2,2,2,2] => 0
[3,3,3,3,3,3,2] => 2
[4,4,3,3,3,3] => 0
[4,4,4,4,4] => 4
[5,5,5,5] => 0
[20] => 20
[10,10] => 0
[8,2,2,2,2,2,2] => 8
[8,6,4,2] => 4
[8,6,6] => 8
[10,6,4] => 8
[9,8,3] => 4
[6,6,6,2] => 4
[10,7,3] => 6
[9,7,4] => 6
[9,5,5,1] => 8
[12,5,1,1,1] => 8
[11,1,1,1,1,1,1,1,1,1] => 10
[6,5,4,3,2,1] => 3
[6,3,3,3,3,2,1] => 5
[6,5,3,2,2,2,1] => 3
[6,5,4,3,1,1,1] => 3
[7,6,2,2,2,2] => 1
[6,6,5,4] => 1
[3,3,3,3,3,3,3] => 3
[4,4,4,3,3,3] => 1
[21] => 21
[11,7,3] => 7
[5,4,2,2,2,2,2,2] => 1
[11,10] => 1
[13,4,4] => 13
[7,6,6,2] => 5
[4,4,4,4,3,2,1] => 2
[6,4,3,3,3,2,1] => 4
[6,5,4,2,2,2,1] => 4
[6,5,4,3,2,1,1] => 4
[4,4,4,4,3,3] => 0
[8,6,2,2,2,2] => 2
[22] => 22
[9,6,4,3] => 4
[8,7,7] => 8
[5,4,4,4,3,2,1] => 3
[6,5,3,3,3,2,1] => 3
[6,5,4,3,2,2,1] => 3
[15,2,2,2,2] => 15
[9,6,5,3] => 5
[8,6,5,3,1] => 5
[6,4,4,4,3,2,1] => 4
[6,5,4,3,3,2,1] => 4
[3,3,3,3,3,3,3,3] => 0
[4,4,4,4,4,4] => 0
[6,6,6,6] => 0
[24] => 24
[11,7,5,1] => 8
[9,7,5,3] => 4
[8,8,8] => 8
[3,3,3,3,3,3,3,2,1] => 2
[17,7] => 10
[12,9,3] => 6
[9,8,1,1,1,1,1,1,1] => 2
[13,1,1,1,1,1,1,1,1,1,1,1] => 12
[5,5,5,4,3,2,1] => 3
[6,5,4,4,3,2,1] => 3
[7,6,6,6] => 1
[5,4,4,4,2,2,2,2] => 1
[13,12] => 1
[15,5,5] => 15
[9,7,5,3,1] => 5
[10,7,5,3] => 5
[3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] => 3
[5,5,5,5,5] => 5
[12,10,3] => 5
[11,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 11
[6,5,5,4,3,2,1] => 4
[6,6,4,3,3,2,2] => 4
[8,6,6,6] => 2
[9,7,5,4,1] => 4
[16,8,2] => 10
[6,6,5,4,3,2,1] => 3
[7,6,5,4,3,2] => 3
[3,3,3,3,3,3,3,3,3] => 3
[15,6,6] => 15
[7,6,5,4,3,2,1] => 4
[6,6,6,4,3,3] => 2
[4,3,3,3,3,3,3,3,3] => 4
[7,6,5,4,3,1,1,1] => 4
[10,7,6,4,1] => 6
[9,7,6,4,2] => 6
[10,8,5,4,1] => 4
[15,14] => 1
[7,6,5,4,3,2,1,1] => 3
[7,6,5,4,2,2,2,1] => 3
[10,8,6,4,1] => 5
[6,6,6,6,6] => 6
[30] => 30
[15,15] => 0
[5,5,5,5,5,5] => 0
[6,6,6,6,3,3] => 0
[10,10,10] => 10
[9,7,5,5,3,1] => 4
[7,6,5,4,3,2,2,1] => 4
[7,6,5,3,3,3,2,1] => 4
[11,8,6,4,1] => 6
[10,8,6,4,2] => 6
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 2
[3,3,3,3,3,3,3,3,3,2,1] => 2
[7,6,6,6,6] => 7
[7,6,5,4,3,3,2,1] => 3
[7,6,4,4,4,3,2,1] => 3
[11,8,6,5,1] => 5
[10,10,9,2] => 7
[14,9,8] => 13
[4,4,4,4,4,4,4,4] => 0
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 0
[7,6,5,4,4,3,2,1] => 4
[7,5,5,5,4,3,2,1] => 4
[16,16] => 0
[10,10,10,2] => 8
[16,8,4,2,2] => 12
[9,4,4,4,4,4,2,1] => 6
[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 1
[5,4,4,4,4,4,4,4] => 1
[7,6,5,5,4,3,2,1] => 3
[6,6,6,5,4,3,2,1] => 3
[22,7,4] => 19
[12,12,4,3,2] => 3
[4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 2
[7,6,6,5,4,3,2,1] => 4
[12,9,7,5,1] => 6
[7,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 7
[7,7,6,5,4,3,2,1] => 3
[13,9,7,5,1] => 7
[18,18] => 0
[24,12] => 12
[11,9,7,5,3,1] => 6
[11,8,7,5,4,1] => 8
[8,7,6,5,4,3,2,1] => 4
[8,7,7,7,7] => 8
[7,6,2,2,2,2,2,2,2,2,2,2,2,2] => 1
[7,6,6,6,6,6] => 1
[8,7,6,5,4,3,2,1,1] => 5
[8,7,6,5,4,3,2,2,1] => 4
[8,7,6,5,4,3,3,2,1] => 5
[10,10,10,10] => 0
[12,12,12,4] => 8
[8,7,6,5,4,4,3,2,1] => 4
[11,9,7,5,5,3] => 6
[4,4,4,4,4,4,4,4,4,4] => 0
[14,14,8,4] => 4
[21,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 20
[7,6,6,6,2,2,2,2,2,2,2,2] => 1
[8,7,6,5,5,4,3,2,1] => 5
[9,9,9,9,3,3] => 0
[8,7,6,6,5,4,3,2,1] => 4
[10,10,10,5,5,2] => 8
[16,10,8,8] => 6
[26,9,7] => 24
[8,7,7,6,5,4,3,2,1] => 5
[8,8,7,6,5,4,3,2,1] => 4
[18,18,9] => 9
[9,8,7,6,5,4,3,2,1] => 5
[11,9,7,7,5,3,3] => 7
[48] => 48
[7,6,6,6,6,6,6,6] => 1
[22,9,8,5,5] => 21
[6,6,6,6,6,6,6,3,3,2] => 4
[27,14,9] => 22
[17,14,13,8] => 8
[5,5,5,5,5,5,5,5,5,5,5] => 5
[27,20,8] => 15
[26,13,7,7,2] => 15
[31,12,10,4] => 25
[6,6,6,6,6,6,6,6,6,6] => 0
[5,5,5,5,5,5,5,5,5,5,5,5] => 0
[12,12,12,12,12] => 12
[17,16,2,2,2,2,2,2,2,2,2,2,2,2,2,1] => 2
[12,12,12,12,11,4] => 7
[12,12,12,12,12,4] => 8
[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 1
[11,11,11,11,11,10] => 1
[11,11,11,11,11,11] => 0
[16,14,9,9,9,9] => 2
[8,8,8,8,8,8,8,8,4,2] => 2
[24,24,24] => 24
[16,16,16,16,8,4,2] => 6
[12,12,12,12,12,12,4,4] => 0
[22,20,20,12,8] => 18
[20,20,8,4,4,4,4,4,4,4,4,4] => 4
[33,32,9,9,5] => 6
[18,18,18,18,18] => 18
[18,18,18,18,9,9] => 0
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3] => 0
[56,17,11,10,5] => 45
[33,26,23,12,9] => 27
[22,22,22,10,10,9,4,4] => 13
[22,22,22,10,10,10,4,4] => 12
[12,12,12,12,12,12,12,12,4,3,2] => 3
[24,24,24,24,14] => 14
[76,22,9,6] => 57
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 5
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 0
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 0
[12,12,12,12,12,12,12,12,12,12] => 0
[24,24,24,24,24] => 24
[23,22,21,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,1] => 20
[12,12,12,12,12,12,12,12,12,6,6,6,4,2] => 8
[54,48,18,10,8] => 22
[24,24,24,24,24,24] => 0
[37,33,20,20,13,10,10,10,7] => 14
[42,34,30,22,22,14,2] => 26
[54,52,34,18,11,7] => 22
[65,27,27,25,13,9,6,6] => 44
[18,18,18,18,18,18,18,18,18,18] => 0
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 0
[16,16,16,16,16,16,16,8,8,8,8,8,8,8,8,4,2] => 14
[58,38,38,38,30] => 50
[12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12] => 0
[10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,2] => 8
[74,58,34,34,22,22,13,11,2] => 20
[61,48,48,48,45,22,12,2] => 46
[15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,5,5,3,3] => 0
[98,62,36,26,14,14,14,14,14,14,12,2] => 56
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,13,2] => 11
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,2] => 12
[74,74,26,26,26,26,12,12,12,12,12,12,6,6,4,4,3,3,3,3] => 0
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 0
[64,57,40,39,28,23,19,19,16,9,8,8,8,8,8,8,6,6] => 20
[70,70,46,28,22,22,10,9,9,9,9,8,8,8,8,8,7,7,7,3,3,3] => 24
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,7,7,7,7,7,2] => 5
[170,92,36,28,27,24,20,14,13,10,8,8] => 98
[12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,6,6,6,6,4,4,4,3,3] => 8
[145,83,62,44,44,42,19,16,16,10,8] => 99
[98,98,37,37,37,37,24,24,24,24,24,24,24,24,10,10,8,8] => 0
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 0
[11,9,7,6,5,3,1] => 6
[13,11,9,7,5,3,1] => 7
[13,11,9,7,7,5,3,1] => 8
[17,13,11,9,7,5,1] => 9
[15,13,11,9,7,5,3,1] => 8
[29,23,19,17,13,11,7,1] => 16
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Created: Oct 17, 2017 at 11:36 by Christian Stump
-----------------------------------------------------------------------------
Last Updated: Jun 19, 2025 at 13:21 by Martin Rubey