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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 *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St000549
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The number of odd partial sums of an integer partition.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(l):
return len(set(sum(l[i] for i in X) for X in Subsets(range(len(l))) if is_odd(sum(l[i] for i in X))))
-----------------------------------------------------------------------------
Statistic values:
[] => 0
[1] => 1
[2] => 0
[1,1] => 1
[3] => 1
[2,1] => 2
[1,1,1] => 2
[4] => 0
[3,1] => 2
[2,2] => 0
[2,1,1] => 2
[1,1,1,1] => 2
[5] => 1
[4,1] => 2
[3,2] => 2
[3,1,1] => 3
[2,2,1] => 3
[2,1,1,1] => 3
[1,1,1,1,1] => 3
[6] => 0
[5,1] => 2
[4,2] => 0
[4,1,1] => 2
[3,3] => 1
[3,2,1] => 3
[3,1,1,1] => 3
[2,2,2] => 0
[2,2,1,1] => 3
[2,1,1,1,1] => 3
[1,1,1,1,1,1] => 3
[7] => 1
[6,1] => 2
[5,2] => 2
[5,1,1] => 3
[4,3] => 2
[4,2,1] => 4
[4,1,1,1] => 4
[3,3,1] => 3
[3,2,2] => 3
[3,2,1,1] => 4
[3,1,1,1,1] => 4
[2,2,2,1] => 4
[2,2,1,1,1] => 4
[2,1,1,1,1,1] => 4
[1,1,1,1,1,1,1] => 4
[8] => 0
[7,1] => 2
[6,2] => 0
[6,1,1] => 2
[5,3] => 2
[5,2,1] => 4
[5,1,1,1] => 4
[4,4] => 0
[4,3,1] => 4
[4,2,2] => 0
[4,2,1,1] => 4
[4,1,1,1,1] => 4
[3,3,2] => 2
[3,3,1,1] => 4
[3,2,2,1] => 4
[3,2,1,1,1] => 4
[3,1,1,1,1,1] => 4
[2,2,2,2] => 0
[2,2,2,1,1] => 4
[2,2,1,1,1,1] => 4
[2,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1] => 4
[9] => 1
[8,1] => 2
[7,2] => 2
[7,1,1] => 3
[6,3] => 2
[6,2,1] => 4
[6,1,1,1] => 4
[5,4] => 2
[5,3,1] => 4
[5,2,2] => 3
[5,2,1,1] => 5
[5,1,1,1,1] => 5
[4,4,1] => 3
[4,3,2] => 4
[4,3,1,1] => 5
[4,2,2,1] => 5
[4,2,1,1,1] => 5
[4,1,1,1,1,1] => 5
[3,3,3] => 2
[3,3,2,1] => 5
[3,3,1,1,1] => 5
[3,2,2,2] => 4
[3,2,2,1,1] => 5
[3,2,1,1,1,1] => 5
[3,1,1,1,1,1,1] => 5
[2,2,2,2,1] => 5
[2,2,2,1,1,1] => 5
[2,2,1,1,1,1,1] => 5
[2,1,1,1,1,1,1,1] => 5
[1,1,1,1,1,1,1,1,1] => 5
[10] => 0
[9,1] => 2
[8,2] => 0
[8,1,1] => 2
[7,3] => 2
[7,2,1] => 4
[7,1,1,1] => 4
[6,4] => 0
[6,3,1] => 4
[6,2,2] => 0
[6,2,1,1] => 4
[6,1,1,1,1] => 4
[5,5] => 1
[5,4,1] => 3
[5,3,2] => 3
[5,3,1,1] => 5
[5,2,2,1] => 5
[5,2,1,1,1] => 5
[5,1,1,1,1,1] => 5
[4,4,2] => 0
[4,4,1,1] => 3
[4,3,3] => 2
[4,3,2,1] => 5
[4,3,1,1,1] => 5
[4,2,2,2] => 0
[4,2,2,1,1] => 5
[4,2,1,1,1,1] => 5
[4,1,1,1,1,1,1] => 5
[3,3,3,1] => 4
[3,3,2,2] => 3
[3,3,2,1,1] => 5
[3,3,1,1,1,1] => 5
[3,2,2,2,1] => 5
[3,2,2,1,1,1] => 5
[3,2,1,1,1,1,1] => 5
[3,1,1,1,1,1,1,1] => 5
[2,2,2,2,2] => 0
[2,2,2,2,1,1] => 5
[2,2,2,1,1,1,1] => 5
[2,2,1,1,1,1,1,1] => 5
[2,1,1,1,1,1,1,1,1] => 5
[1,1,1,1,1,1,1,1,1,1] => 5
[11] => 1
[10,1] => 2
[9,2] => 2
[9,1,1] => 3
[8,3] => 2
[8,2,1] => 4
[8,1,1,1] => 4
[7,4] => 2
[7,3,1] => 4
[7,2,2] => 3
[7,2,1,1] => 5
[7,1,1,1,1] => 5
[6,5] => 2
[6,4,1] => 4
[6,3,2] => 4
[6,3,1,1] => 6
[6,2,2,1] => 6
[6,2,1,1,1] => 6
[6,1,1,1,1,1] => 6
[5,5,1] => 3
[5,4,2] => 4
[5,4,1,1] => 5
[5,3,3] => 3
[5,3,2,1] => 6
[5,3,1,1,1] => 6
[5,2,2,2] => 4
[5,2,2,1,1] => 6
[5,2,1,1,1,1] => 6
[5,1,1,1,1,1,1] => 6
[4,4,3] => 3
[4,4,2,1] => 6
[4,4,1,1,1] => 6
[4,3,3,1] => 5
[4,3,2,2] => 5
[4,3,2,1,1] => 6
[4,3,1,1,1,1] => 6
[4,2,2,2,1] => 6
[4,2,2,1,1,1] => 6
[4,2,1,1,1,1,1] => 6
[4,1,1,1,1,1,1,1] => 6
[3,3,3,2] => 4
[3,3,3,1,1] => 6
[3,3,2,2,1] => 6
[3,3,2,1,1,1] => 6
[3,3,1,1,1,1,1] => 6
[3,2,2,2,2] => 5
[3,2,2,2,1,1] => 6
[3,2,2,1,1,1,1] => 6
[3,2,1,1,1,1,1,1] => 6
[3,1,1,1,1,1,1,1,1] => 6
[2,2,2,2,2,1] => 6
[2,2,2,2,1,1,1] => 6
[2,2,2,1,1,1,1,1] => 6
[2,2,1,1,1,1,1,1,1] => 6
[2,1,1,1,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,1,1,1,1] => 6
[12] => 0
[11,1] => 2
[10,2] => 0
[10,1,1] => 2
[9,3] => 2
[9,2,1] => 4
[9,1,1,1] => 4
[8,4] => 0
[8,3,1] => 4
[8,2,2] => 0
[8,2,1,1] => 4
[8,1,1,1,1] => 4
[7,5] => 2
[7,4,1] => 4
[7,3,2] => 4
[7,3,1,1] => 6
[7,2,2,1] => 6
[7,2,1,1,1] => 6
[7,1,1,1,1,1] => 6
[6,6] => 0
[6,5,1] => 4
[6,4,2] => 0
[6,4,1,1] => 4
[6,3,3] => 2
[6,3,2,1] => 6
[6,3,1,1,1] => 6
[6,2,2,2] => 0
[6,2,2,1,1] => 6
[6,2,1,1,1,1] => 6
[6,1,1,1,1,1,1] => 6
[5,5,2] => 2
[5,5,1,1] => 4
[5,4,3] => 4
[5,4,2,1] => 6
[5,4,1,1,1] => 6
[5,3,3,1] => 6
[5,3,2,2] => 4
[5,3,2,1,1] => 6
[5,3,1,1,1,1] => 6
[5,2,2,2,1] => 6
[5,2,2,1,1,1] => 6
[5,2,1,1,1,1,1] => 6
[5,1,1,1,1,1,1,1] => 6
[4,4,4] => 0
[4,4,3,1] => 6
[4,4,2,2] => 0
[4,4,2,1,1] => 6
[4,4,1,1,1,1] => 6
[4,3,3,2] => 4
[4,3,3,1,1] => 6
[4,3,2,2,1] => 6
[4,3,2,1,1,1] => 6
[4,3,1,1,1,1,1] => 6
[4,2,2,2,2] => 0
[4,2,2,2,1,1] => 6
[4,2,2,1,1,1,1] => 6
[4,2,1,1,1,1,1,1] => 6
[4,1,1,1,1,1,1,1,1] => 6
[3,3,3,3] => 2
[3,3,3,2,1] => 6
[3,3,3,1,1,1] => 6
[3,3,2,2,2] => 4
[3,3,2,2,1,1] => 6
[3,3,2,1,1,1,1] => 6
[3,3,1,1,1,1,1,1] => 6
[3,2,2,2,2,1] => 6
[3,2,2,2,1,1,1] => 6
[3,2,2,1,1,1,1,1] => 6
[3,2,1,1,1,1,1,1,1] => 6
[3,1,1,1,1,1,1,1,1,1] => 6
[2,2,2,2,2,2] => 0
[2,2,2,2,2,1,1] => 6
[2,2,2,2,1,1,1,1] => 6
[2,2,2,1,1,1,1,1,1] => 6
[2,2,1,1,1,1,1,1,1,1] => 6
[2,1,1,1,1,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,1,1,1,1,1] => 6
[8,5] => 2
[7,6] => 2
[7,5,1] => 4
[7,4,2] => 4
[6,6,1] => 3
[6,4,2,1] => 7
[5,5,3] => 3
[5,4,4] => 3
[5,4,3,1] => 6
[5,4,2,2] => 5
[5,4,2,1,1] => 7
[5,4,1,1,1,1] => 7
[5,3,3,2] => 5
[5,3,3,1,1] => 7
[5,3,2,2,1] => 7
[5,3,2,1,1,1] => 7
[4,4,4,1] => 4
[4,4,3,2] => 6
[4,4,3,1,1] => 7
[4,4,2,2,1] => 7
[4,3,3,3] => 4
[4,3,3,2,1] => 7
[3,3,3,3,1] => 5
[3,3,3,2,2] => 6
[3,3,2,2,2,1] => 7
[3,2,2,2,2,2] => 6
[2,2,2,2,2,2,1] => 7
[9,5] => 2
[8,5,1] => 4
[7,7] => 1
[7,5,2] => 3
[7,4,3] => 3
[6,6,2] => 0
[6,4,4] => 0
[6,2,2,2,2] => 0
[5,5,4] => 2
[5,5,1,1,1,1] => 7
[5,4,3,2] => 5
[5,4,3,1,1] => 7
[5,4,2,2,1] => 7
[5,4,2,1,1,1] => 7
[5,3,3,3] => 4
[5,3,3,2,1] => 7
[5,2,2,2,2,1] => 7
[4,4,4,2] => 0
[4,4,3,3] => 3
[4,4,3,2,1] => 7
[4,3,2,2,2,1] => 7
[3,3,3,3,2] => 4
[3,3,3,3,1,1] => 7
[3,3,2,2,2,2] => 5
[2,2,2,2,2,2,2] => 0
[9,5,1] => 4
[8,5,2] => 4
[7,5,3] => 4
[6,6,3] => 3
[6,5,4] => 4
[6,5,1,1,1,1] => 8
[6,3,3,3] => 3
[6,2,2,2,2,1] => 8
[5,5,5] => 2
[5,4,3,3] => 6
[5,4,3,2,1] => 8
[5,4,3,1,1,1] => 8
[5,3,2,2,2,1] => 8
[4,4,4,3] => 4
[4,4,4,1,1,1] => 8
[4,3,3,3,2] => 7
[3,3,3,3,3] => 3
[3,3,3,3,2,1] => 8
[3,3,3,2,2,2] => 7
[8,8] => 0
[8,5,3] => 4
[7,5,3,1] => 8
[6,6,4] => 0
[5,5,3,3] => 4
[5,5,2,2,2] => 4
[5,4,4,3] => 6
[5,4,3,2,1,1] => 8
[5,4,2,2,2,1] => 8
[4,4,4,4] => 0
[4,4,4,2,2] => 0
[4,4,3,3,2] => 6
[4,3,3,3,3] => 4
[4,3,3,3,2,1] => 8
[3,3,3,3,2,2] => 6
[2,2,2,2,2,2,2,2] => 0
[8,6,3] => 4
[7,5,3,2] => 6
[6,5,3,3] => 5
[6,5,2,2,2] => 7
[6,4,4,3] => 6
[6,4,4,1,1,1] => 9
[6,3,3,3,2] => 6
[6,3,3,3,1,1] => 9
[5,5,4,3] => 6
[5,5,4,1,1,1] => 9
[5,5,2,2,2,1] => 9
[5,4,4,4] => 4
[5,4,3,2,2,1] => 9
[5,3,3,3,2,1] => 9
[4,4,4,3,2] => 8
[4,4,4,3,1,1] => 9
[4,4,4,2,2,1] => 9
[4,4,3,3,3] => 6
[3,3,3,3,3,2] => 6
[4,4,4,3,2,1] => 9
[5,4,3,3,2,1] => 9
[6,3,3,3,2,1] => 9
[6,5,2,2,2,1] => 9
[5,5,3,3,1,1] => 9
[6,5,4,1,1,1] => 9
[5,5,3,3,2] => 6
[5,5,4,2,2] => 5
[6,4,4,2,2] => 0
[6,5,4,3] => 7
[4,4,4,3,3] => 4
[4,4,4,4,2] => 0
[5,5,4,4] => 3
[2,2,2,2,2,2,2,2,2] => 0
[3,3,3,3,3,3] => 3
[6,6,6] => 0
[9,6,3] => 3
[8,6,4] => 0
[9,9] => 1
[5,4,4,3,2,1] => 10
[5,5,3,3,2,1] => 10
[5,5,4,2,2,1] => 10
[6,4,4,2,2,1] => 10
[5,5,4,3,1,1] => 10
[6,4,4,3,1,1] => 10
[6,5,3,3,1,1] => 10
[5,5,4,3,2] => 9
[6,4,4,3,2] => 9
[6,5,3,3,2] => 8
[6,5,4,2,2] => 8
[6,5,4,3,1] => 9
[6,5,4,1,1,1,1] => 10
[4,4,4,4,3] => 5
[4,3,3,3,3,3] => 6
[9,6,4] => 4
[8,5,4,2] => 8
[8,5,5,1] => 6
[5,5,4,3,2,1] => 10
[6,4,4,3,2,1] => 10
[6,5,3,3,2,1] => 10
[6,5,4,2,2,1] => 10
[6,5,4,3,1,1] => 10
[6,5,4,3,2] => 8
[6,5,2,2,2,2,1] => 10
[6,5,4,2,1,1,1] => 10
[7,5,4,3,1] => 10
[3,3,3,3,3,3,2] => 6
[4,4,3,3,3,3] => 6
[4,4,4,4,4] => 0
[5,5,5,5] => 2
[8,6,4,2] => 0
[10,6,4] => 0
[10,7,3] => 4
[9,7,4] => 4
[9,5,5,1] => 6
[6,5,4,3,2,1] => 11
[6,3,3,3,3,2,1] => 11
[6,5,3,2,2,2,1] => 11
[6,5,4,3,1,1,1] => 11
[3,3,3,3,3,3,3] => 4
[4,4,4,3,3,3] => 8
[11,7,3] => 4
[4,4,4,4,3,2,1] => 11
[6,4,3,3,3,2,1] => 11
[6,5,4,2,2,2,1] => 11
[6,5,4,3,2,1,1] => 11
[4,4,4,4,3,3] => 5
[9,6,4,3] => 6
[5,4,4,4,3,2,1] => 12
[6,5,3,3,3,2,1] => 12
[6,5,4,3,2,2,1] => 12
[9,6,5,3] => 7
[8,6,5,3,1] => 11
[6,4,4,4,3,2,1] => 12
[6,5,4,3,3,2,1] => 12
[3,3,3,3,3,3,3,3] => 4
[4,4,4,4,4,4] => 0
[11,7,5,1] => 8
[9,7,5,3] => 8
[8,8,8] => 0
[5,5,5,4,3,2,1] => 13
[6,5,4,4,3,2,1] => 13
[9,7,5,3,1] => 12
[10,7,5,3] => 7
[6,5,5,4,3,2,1] => 13
[9,7,5,4,1] => 11
[6,6,5,4,3,2,1] => 14
[7,6,5,4,3,2] => 13
[3,3,3,3,3,3,3,3,3] => 5
[7,6,5,4,3,2,1] => 14
[7,6,5,4,3,1,1,1] => 14
[10,7,6,4,1] => 10
[9,7,6,4,2] => 8
[10,8,5,4,1] => 10
[7,6,5,4,3,2,1,1] => 15
[7,6,5,4,2,2,2,1] => 15
[10,8,6,4,1] => 13
[9,7,5,5,3,1] => 15
[7,6,5,4,3,2,2,1] => 15
[7,6,5,3,3,3,2,1] => 15
[11,8,6,4,1] => 13
[10,8,6,4,2] => 0
[7,6,5,4,3,3,2,1] => 16
[7,6,4,4,4,3,2,1] => 16
[11,8,6,5,1] => 12
[4,4,4,4,4,4,4,4] => 0
[7,6,5,4,4,3,2,1] => 16
[7,5,5,5,4,3,2,1] => 16
[7,6,5,5,4,3,2,1] => 17
[6,6,6,5,4,3,2,1] => 17
[7,6,6,5,4,3,2,1] => 17
[12,9,7,5,1] => 13
[7,7,6,5,4,3,2,1] => 18
[13,9,7,5,1] => 14
[11,9,7,5,3,1] => 18
[11,8,7,5,4,1] => 16
[8,7,6,5,4,3,2,1] => 18
[8,7,6,5,4,3,2,1,1] => 19
[8,7,6,5,4,3,2,2,1] => 19
[8,7,6,5,4,3,3,2,1] => 20
[8,7,6,5,4,4,3,2,1] => 20
[11,9,7,5,5,3] => 18
[8,7,6,5,5,4,3,2,1] => 21
[8,7,6,6,5,4,3,2,1] => 21
[8,7,7,6,5,4,3,2,1] => 22
[8,8,7,6,5,4,3,2,1] => 22
[9,8,7,6,5,4,3,2,1] => 23
[11,9,7,7,5,3,3] => 20
-----------------------------------------------------------------------------
Created: Jul 16, 2016 at 16:42 by Christian Stump
-----------------------------------------------------------------------------
Last Updated: Dec 10, 2022 at 14:48 by Martin Rubey