*****************************************************************************
* 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: St001127
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The sum of the squares of the parts of a partition.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(pi):
return sum(p^2 for p in pi)
-----------------------------------------------------------------------------
Statistic values:
[] => 0
[1] => 1
[2] => 4
[1,1] => 2
[3] => 9
[2,1] => 5
[1,1,1] => 3
[4] => 16
[3,1] => 10
[2,2] => 8
[2,1,1] => 6
[1,1,1,1] => 4
[5] => 25
[4,1] => 17
[3,2] => 13
[3,1,1] => 11
[2,2,1] => 9
[2,1,1,1] => 7
[1,1,1,1,1] => 5
[6] => 36
[5,1] => 26
[4,2] => 20
[4,1,1] => 18
[3,3] => 18
[3,2,1] => 14
[3,1,1,1] => 12
[2,2,2] => 12
[2,2,1,1] => 10
[2,1,1,1,1] => 8
[1,1,1,1,1,1] => 6
[7] => 49
[6,1] => 37
[5,2] => 29
[5,1,1] => 27
[4,3] => 25
[4,2,1] => 21
[4,1,1,1] => 19
[3,3,1] => 19
[3,2,2] => 17
[3,2,1,1] => 15
[3,1,1,1,1] => 13
[2,2,2,1] => 13
[2,2,1,1,1] => 11
[2,1,1,1,1,1] => 9
[1,1,1,1,1,1,1] => 7
[8] => 64
[7,1] => 50
[6,2] => 40
[6,1,1] => 38
[5,3] => 34
[5,2,1] => 30
[5,1,1,1] => 28
[4,4] => 32
[4,3,1] => 26
[4,2,2] => 24
[4,2,1,1] => 22
[4,1,1,1,1] => 20
[3,3,2] => 22
[3,3,1,1] => 20
[3,2,2,1] => 18
[3,2,1,1,1] => 16
[3,1,1,1,1,1] => 14
[2,2,2,2] => 16
[2,2,2,1,1] => 14
[2,2,1,1,1,1] => 12
[2,1,1,1,1,1,1] => 10
[1,1,1,1,1,1,1,1] => 8
[9] => 81
[8,1] => 65
[7,2] => 53
[7,1,1] => 51
[6,3] => 45
[6,2,1] => 41
[6,1,1,1] => 39
[5,4] => 41
[5,3,1] => 35
[5,2,2] => 33
[5,2,1,1] => 31
[5,1,1,1,1] => 29
[4,4,1] => 33
[4,3,2] => 29
[4,3,1,1] => 27
[4,2,2,1] => 25
[4,2,1,1,1] => 23
[4,1,1,1,1,1] => 21
[3,3,3] => 27
[3,3,2,1] => 23
[3,3,1,1,1] => 21
[3,2,2,2] => 21
[3,2,2,1,1] => 19
[3,2,1,1,1,1] => 17
[3,1,1,1,1,1,1] => 15
[2,2,2,2,1] => 17
[2,2,2,1,1,1] => 15
[2,2,1,1,1,1,1] => 13
[2,1,1,1,1,1,1,1] => 11
[1,1,1,1,1,1,1,1,1] => 9
[10] => 100
[9,1] => 82
[8,2] => 68
[8,1,1] => 66
[7,3] => 58
[7,2,1] => 54
[7,1,1,1] => 52
[6,4] => 52
[6,3,1] => 46
[6,2,2] => 44
[6,2,1,1] => 42
[6,1,1,1,1] => 40
[5,5] => 50
[5,4,1] => 42
[5,3,2] => 38
[5,3,1,1] => 36
[5,2,2,1] => 34
[5,2,1,1,1] => 32
[5,1,1,1,1,1] => 30
[4,4,2] => 36
[4,4,1,1] => 34
[4,3,3] => 34
[4,3,2,1] => 30
[4,3,1,1,1] => 28
[4,2,2,2] => 28
[4,2,2,1,1] => 26
[4,2,1,1,1,1] => 24
[4,1,1,1,1,1,1] => 22
[3,3,3,1] => 28
[3,3,2,2] => 26
[3,3,2,1,1] => 24
[3,3,1,1,1,1] => 22
[3,2,2,2,1] => 22
[3,2,2,1,1,1] => 20
[3,2,1,1,1,1,1] => 18
[3,1,1,1,1,1,1,1] => 16
[2,2,2,2,2] => 20
[2,2,2,2,1,1] => 18
[2,2,2,1,1,1,1] => 16
[2,2,1,1,1,1,1,1] => 14
[2,1,1,1,1,1,1,1,1] => 12
[1,1,1,1,1,1,1,1,1,1] => 10
[11] => 121
[10,1] => 101
[9,2] => 85
[9,1,1] => 83
[8,3] => 73
[8,2,1] => 69
[8,1,1,1] => 67
[7,4] => 65
[7,3,1] => 59
[7,2,2] => 57
[7,2,1,1] => 55
[7,1,1,1,1] => 53
[6,5] => 61
[6,4,1] => 53
[6,3,2] => 49
[6,3,1,1] => 47
[6,2,2,1] => 45
[6,2,1,1,1] => 43
[6,1,1,1,1,1] => 41
[5,5,1] => 51
[5,4,2] => 45
[5,4,1,1] => 43
[5,3,3] => 43
[5,3,2,1] => 39
[5,3,1,1,1] => 37
[5,2,2,2] => 37
[5,2,2,1,1] => 35
[5,2,1,1,1,1] => 33
[5,1,1,1,1,1,1] => 31
[4,4,3] => 41
[4,4,2,1] => 37
[4,4,1,1,1] => 35
[4,3,3,1] => 35
[4,3,2,2] => 33
[4,3,2,1,1] => 31
[4,3,1,1,1,1] => 29
[4,2,2,2,1] => 29
[4,2,2,1,1,1] => 27
[4,2,1,1,1,1,1] => 25
[4,1,1,1,1,1,1,1] => 23
[3,3,3,2] => 31
[3,3,3,1,1] => 29
[3,3,2,2,1] => 27
[3,3,2,1,1,1] => 25
[3,3,1,1,1,1,1] => 23
[3,2,2,2,2] => 25
[3,2,2,2,1,1] => 23
[3,2,2,1,1,1,1] => 21
[3,2,1,1,1,1,1,1] => 19
[3,1,1,1,1,1,1,1,1] => 17
[2,2,2,2,2,1] => 21
[2,2,2,2,1,1,1] => 19
[2,2,2,1,1,1,1,1] => 17
[2,2,1,1,1,1,1,1,1] => 15
[2,1,1,1,1,1,1,1,1,1] => 13
[1,1,1,1,1,1,1,1,1,1,1] => 11
[12] => 144
[11,1] => 122
[10,2] => 104
[10,1,1] => 102
[9,3] => 90
[9,2,1] => 86
[9,1,1,1] => 84
[8,4] => 80
[8,3,1] => 74
[8,2,2] => 72
[8,2,1,1] => 70
[8,1,1,1,1] => 68
[7,5] => 74
[7,4,1] => 66
[7,3,2] => 62
[7,3,1,1] => 60
[7,2,2,1] => 58
[7,2,1,1,1] => 56
[7,1,1,1,1,1] => 54
[6,6] => 72
[6,5,1] => 62
[6,4,2] => 56
[6,4,1,1] => 54
[6,3,3] => 54
[6,3,2,1] => 50
[6,3,1,1,1] => 48
[6,2,2,2] => 48
[6,2,2,1,1] => 46
[6,2,1,1,1,1] => 44
[6,1,1,1,1,1,1] => 42
[5,5,2] => 54
[5,5,1,1] => 52
[5,4,3] => 50
[5,4,2,1] => 46
[5,4,1,1,1] => 44
[5,3,3,1] => 44
[5,3,2,2] => 42
[5,3,2,1,1] => 40
[5,3,1,1,1,1] => 38
[5,2,2,2,1] => 38
[5,2,2,1,1,1] => 36
[5,2,1,1,1,1,1] => 34
[5,1,1,1,1,1,1,1] => 32
[4,4,4] => 48
[4,4,3,1] => 42
[4,4,2,2] => 40
[4,4,2,1,1] => 38
[4,4,1,1,1,1] => 36
[4,3,3,2] => 38
[4,3,3,1,1] => 36
[4,3,2,2,1] => 34
[4,3,2,1,1,1] => 32
[4,3,1,1,1,1,1] => 30
[4,2,2,2,2] => 32
[4,2,2,2,1,1] => 30
[4,2,2,1,1,1,1] => 28
[4,2,1,1,1,1,1,1] => 26
[4,1,1,1,1,1,1,1,1] => 24
[3,3,3,3] => 36
[3,3,3,2,1] => 32
[3,3,3,1,1,1] => 30
[3,3,2,2,2] => 30
[3,3,2,2,1,1] => 28
[3,3,2,1,1,1,1] => 26
[3,3,1,1,1,1,1,1] => 24
[3,2,2,2,2,1] => 26
[3,2,2,2,1,1,1] => 24
[3,2,2,1,1,1,1,1] => 22
[3,2,1,1,1,1,1,1,1] => 20
[3,1,1,1,1,1,1,1,1,1] => 18
[2,2,2,2,2,2] => 24
[2,2,2,2,2,1,1] => 22
[2,2,2,2,1,1,1,1] => 20
[2,2,2,1,1,1,1,1,1] => 18
[2,2,1,1,1,1,1,1,1,1] => 16
[2,1,1,1,1,1,1,1,1,1,1] => 14
[1,1,1,1,1,1,1,1,1,1,1,1] => 12
[5,4,3,1] => 51
[5,4,2,2] => 49
[5,4,2,1,1] => 47
[5,3,3,2] => 47
[5,3,3,1,1] => 45
[5,3,2,2,1] => 43
[4,4,3,2] => 45
[4,4,3,1,1] => 43
[4,4,2,2,1] => 41
[4,3,3,2,1] => 39
[5,4,3,2] => 54
[5,4,3,1,1] => 52
[5,4,2,2,1] => 50
[5,3,3,2,1] => 48
[4,4,3,2,1] => 46
[5,4,3,2,1] => 55
-----------------------------------------------------------------------------
Created: Mar 20, 2018 at 16:22 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Apr 26, 2018 at 07:41 by Martin Rubey