edit this statistic or download as text // json
Identifier
Values
=>
[1]=>1 [1,1]=>2 [1,2]=>3 [2,1]=>3 [1,1,1]=>3 [1,1,2]=>4 [1,2,1]=>4 [2,1,1]=>4 [1,1,3]=>5 [1,3,1]=>5 [3,1,1]=>5 [1,2,2]=>5 [2,1,2]=>5 [2,2,1]=>5 [1,2,3]=>6 [1,3,2]=>6 [2,1,3]=>6 [2,3,1]=>6 [3,1,2]=>6 [3,2,1]=>6 [1,1,1,1]=>4 [1,1,1,2]=>5 [1,1,2,1]=>5 [1,2,1,1]=>5 [2,1,1,1]=>5 [1,1,1,3]=>6 [1,1,3,1]=>6 [1,3,1,1]=>6 [3,1,1,1]=>6 [1,1,1,4]=>7 [1,1,4,1]=>7 [1,4,1,1]=>7 [4,1,1,1]=>7 [1,1,2,2]=>6 [1,2,1,2]=>6 [1,2,2,1]=>6 [2,1,1,2]=>6 [2,1,2,1]=>6 [2,2,1,1]=>6 [1,1,2,3]=>7 [1,1,3,2]=>7 [1,2,1,3]=>7 [1,2,3,1]=>7 [1,3,1,2]=>7 [1,3,2,1]=>7 [2,1,1,3]=>7 [2,1,3,1]=>7 [2,3,1,1]=>7 [3,1,1,2]=>7 [3,1,2,1]=>7 [3,2,1,1]=>7 [1,1,2,4]=>8 [1,1,4,2]=>8 [1,2,1,4]=>8 [1,2,4,1]=>8 [1,4,1,2]=>8 [1,4,2,1]=>8 [2,1,1,4]=>8 [2,1,4,1]=>8 [2,4,1,1]=>8 [4,1,1,2]=>8 [4,1,2,1]=>8 [4,2,1,1]=>8 [1,1,3,3]=>8 [1,3,1,3]=>8 [1,3,3,1]=>8 [3,1,1,3]=>8 [3,1,3,1]=>8 [3,3,1,1]=>8 [1,1,3,4]=>9 [1,1,4,3]=>9 [1,3,1,4]=>9 [1,3,4,1]=>9 [1,4,1,3]=>9 [1,4,3,1]=>9 [3,1,1,4]=>9 [3,1,4,1]=>9 [3,4,1,1]=>9 [4,1,1,3]=>9 [4,1,3,1]=>9 [4,3,1,1]=>9 [1,2,2,2]=>7 [2,1,2,2]=>7 [2,2,1,2]=>7 [2,2,2,1]=>7 [1,2,2,3]=>8 [1,2,3,2]=>8 [1,3,2,2]=>8 [2,1,2,3]=>8 [2,1,3,2]=>8 [2,2,1,3]=>8 [2,2,3,1]=>8 [2,3,1,2]=>8 [2,3,2,1]=>8 [3,1,2,2]=>8 [3,2,1,2]=>8 [3,2,2,1]=>8 [1,2,2,4]=>9 [1,2,4,2]=>9 [1,4,2,2]=>9 [2,1,2,4]=>9 [2,1,4,2]=>9 [2,2,1,4]=>9 [2,2,4,1]=>9 [2,4,1,2]=>9 [2,4,2,1]=>9 [4,1,2,2]=>9 [4,2,1,2]=>9 [4,2,2,1]=>9 [1,2,3,3]=>9 [1,3,2,3]=>9 [1,3,3,2]=>9 [2,1,3,3]=>9 [2,3,1,3]=>9 [2,3,3,1]=>9 [3,1,2,3]=>9 [3,1,3,2]=>9 [3,2,1,3]=>9 [3,2,3,1]=>9 [3,3,1,2]=>9 [3,3,2,1]=>9 [1,2,3,4]=>10 [1,2,4,3]=>10 [1,3,2,4]=>10 [1,3,4,2]=>10 [1,4,2,3]=>10 [1,4,3,2]=>10 [2,1,3,4]=>10 [2,1,4,3]=>10 [2,3,1,4]=>10 [2,3,4,1]=>10 [2,4,1,3]=>10 [2,4,3,1]=>10 [3,1,2,4]=>10 [3,1,4,2]=>10 [3,2,1,4]=>10 [3,2,4,1]=>10 [3,4,1,2]=>10 [3,4,2,1]=>10 [4,1,2,3]=>10 [4,1,3,2]=>10 [4,2,1,3]=>10 [4,2,3,1]=>10 [4,3,1,2]=>10 [4,3,2,1]=>10 [1,1,1,1,1]=>5 [1,1,1,1,2]=>6 [1,1,1,2,1]=>6 [1,1,2,1,1]=>6 [1,2,1,1,1]=>6 [2,1,1,1,1]=>6 [1,1,1,1,3]=>7 [1,1,1,3,1]=>7 [1,1,3,1,1]=>7 [1,3,1,1,1]=>7 [3,1,1,1,1]=>7 [1,1,1,1,4]=>8 [1,1,1,4,1]=>8 [1,1,4,1,1]=>8 [1,4,1,1,1]=>8 [4,1,1,1,1]=>8 [1,1,1,1,5]=>9 [1,1,1,5,1]=>9 [1,1,5,1,1]=>9 [1,5,1,1,1]=>9 [5,1,1,1,1]=>9 [1,1,1,2,2]=>7 [1,1,2,1,2]=>7 [1,1,2,2,1]=>7 [1,2,1,1,2]=>7 [1,2,1,2,1]=>7 [1,2,2,1,1]=>7 [2,1,1,1,2]=>7 [2,1,1,2,1]=>7 [2,1,2,1,1]=>7 [2,2,1,1,1]=>7 [1,1,1,2,3]=>8 [1,1,1,3,2]=>8 [1,1,2,1,3]=>8 [1,1,2,3,1]=>8 [1,1,3,1,2]=>8 [1,1,3,2,1]=>8 [1,2,1,1,3]=>8 [1,2,1,3,1]=>8 [1,2,3,1,1]=>8 [1,3,1,1,2]=>8 [1,3,1,2,1]=>8 [1,3,2,1,1]=>8 [2,1,1,1,3]=>8 [2,1,1,3,1]=>8 [2,1,3,1,1]=>8 [2,3,1,1,1]=>8 [3,1,1,1,2]=>8 [3,1,1,2,1]=>8 [3,1,2,1,1]=>8 [3,2,1,1,1]=>8 [1,1,1,2,4]=>9 [1,1,1,4,2]=>9 [1,1,2,1,4]=>9 [1,1,2,4,1]=>9 [1,1,4,1,2]=>9 [1,1,4,2,1]=>9 [1,2,1,1,4]=>9 [1,2,1,4,1]=>9 [1,2,4,1,1]=>9 [1,4,1,1,2]=>9 [1,4,1,2,1]=>9 [1,4,2,1,1]=>9 [2,1,1,1,4]=>9 [2,1,1,4,1]=>9 [2,1,4,1,1]=>9 [2,4,1,1,1]=>9 [4,1,1,1,2]=>9 [4,1,1,2,1]=>9 [4,1,2,1,1]=>9 [4,2,1,1,1]=>9 [1,1,1,2,5]=>10 [1,1,1,5,2]=>10 [1,1,2,1,5]=>10 [1,1,2,5,1]=>10 [1,1,5,1,2]=>10 [1,1,5,2,1]=>10 [1,2,1,1,5]=>10 [1,2,1,5,1]=>10 [1,2,5,1,1]=>10 [1,5,1,1,2]=>10 [1,5,1,2,1]=>10 [1,5,2,1,1]=>10 [2,1,1,1,5]=>10 [2,1,1,5,1]=>10 [2,1,5,1,1]=>10 [2,5,1,1,1]=>10 [5,1,1,1,2]=>10 [5,1,1,2,1]=>10 [5,1,2,1,1]=>10 [5,2,1,1,1]=>10 [1,1,1,3,3]=>9 [1,1,3,1,3]=>9 [1,1,3,3,1]=>9 [1,3,1,1,3]=>9 [1,3,1,3,1]=>9 [1,3,3,1,1]=>9 [3,1,1,1,3]=>9 [3,1,1,3,1]=>9 [3,1,3,1,1]=>9 [3,3,1,1,1]=>9 [1,1,1,3,4]=>10 [1,1,1,4,3]=>10 [1,1,3,1,4]=>10 [1,1,3,4,1]=>10 [1,1,4,1,3]=>10 [1,1,4,3,1]=>10 [1,3,1,1,4]=>10 [1,3,1,4,1]=>10 [1,3,4,1,1]=>10 [1,4,1,1,3]=>10 [1,4,1,3,1]=>10 [1,4,3,1,1]=>10 [3,1,1,1,4]=>10 [3,1,1,4,1]=>10 [3,1,4,1,1]=>10 [3,4,1,1,1]=>10 [4,1,1,1,3]=>10 [4,1,1,3,1]=>10 [4,1,3,1,1]=>10 [4,3,1,1,1]=>10 [1,1,1,3,5]=>11 [1,1,1,5,3]=>11 [1,1,3,1,5]=>11 [1,1,3,5,1]=>11 [1,1,5,1,3]=>11 [1,1,5,3,1]=>11 [1,3,1,1,5]=>11 [1,3,1,5,1]=>11 [1,3,5,1,1]=>11 [1,5,1,1,3]=>11 [1,5,1,3,1]=>11 [1,5,3,1,1]=>11 [3,1,1,1,5]=>11 [3,1,1,5,1]=>11 [3,1,5,1,1]=>11 [3,5,1,1,1]=>11 [5,1,1,1,3]=>11 [5,1,1,3,1]=>11 [5,1,3,1,1]=>11 [5,3,1,1,1]=>11 [1,1,1,4,4]=>11 [1,1,4,1,4]=>11 [1,1,4,4,1]=>11 [1,4,1,1,4]=>11 [1,4,1,4,1]=>11 [1,4,4,1,1]=>11 [4,1,1,1,4]=>11 [4,1,1,4,1]=>11 [4,1,4,1,1]=>11 [4,4,1,1,1]=>11 [1,1,1,4,5]=>12 [1,1,1,5,4]=>12 [1,1,4,1,5]=>12 [1,1,4,5,1]=>12 [1,1,5,1,4]=>12 [1,1,5,4,1]=>12 [1,4,1,1,5]=>12 [1,4,1,5,1]=>12 [1,4,5,1,1]=>12 [1,5,1,1,4]=>12 [1,5,1,4,1]=>12 [1,5,4,1,1]=>12 [4,1,1,1,5]=>12 [4,1,1,5,1]=>12 [4,1,5,1,1]=>12 [4,5,1,1,1]=>12 [5,1,1,1,4]=>12 [5,1,1,4,1]=>12 [5,1,4,1,1]=>12 [5,4,1,1,1]=>12 [1,1,2,2,2]=>8 [1,2,1,2,2]=>8 [1,2,2,1,2]=>8 [1,2,2,2,1]=>8 [2,1,1,2,2]=>8 [2,1,2,1,2]=>8 [2,1,2,2,1]=>8 [2,2,1,1,2]=>8 [2,2,1,2,1]=>8 [2,2,2,1,1]=>8 [1,1,2,2,3]=>9 [1,1,2,3,2]=>9 [1,1,3,2,2]=>9 [1,2,1,2,3]=>9 [1,2,1,3,2]=>9 [1,2,2,1,3]=>9 [1,2,2,3,1]=>9 [1,2,3,1,2]=>9 [1,2,3,2,1]=>9 [1,3,1,2,2]=>9 [1,3,2,1,2]=>9 [1,3,2,2,1]=>9 [2,1,1,2,3]=>9 [2,1,1,3,2]=>9 [2,1,2,1,3]=>9 [2,1,2,3,1]=>9 [2,1,3,1,2]=>9 [2,1,3,2,1]=>9 [2,2,1,1,3]=>9 [2,2,1,3,1]=>9 [2,2,3,1,1]=>9 [2,3,1,1,2]=>9 [2,3,1,2,1]=>9 [2,3,2,1,1]=>9 [3,1,1,2,2]=>9 [3,1,2,1,2]=>9 [3,1,2,2,1]=>9 [3,2,1,1,2]=>9 [3,2,1,2,1]=>9 [3,2,2,1,1]=>9 [1,1,2,2,4]=>10 [1,1,2,4,2]=>10 [1,1,4,2,2]=>10 [1,2,1,2,4]=>10 [1,2,1,4,2]=>10 [1,2,2,1,4]=>10 [1,2,2,4,1]=>10 [1,2,4,1,2]=>10 [1,2,4,2,1]=>10 [1,4,1,2,2]=>10 [1,4,2,1,2]=>10 [1,4,2,2,1]=>10 [2,1,1,2,4]=>10 [2,1,1,4,2]=>10 [2,1,2,1,4]=>10 [2,1,2,4,1]=>10 [2,1,4,1,2]=>10 [2,1,4,2,1]=>10 [2,2,1,1,4]=>10 [2,2,1,4,1]=>10 [2,2,4,1,1]=>10 [2,4,1,1,2]=>10 [2,4,1,2,1]=>10 [2,4,2,1,1]=>10 [4,1,1,2,2]=>10 [4,1,2,1,2]=>10 [4,1,2,2,1]=>10 [4,2,1,1,2]=>10 [4,2,1,2,1]=>10 [4,2,2,1,1]=>10 [1,1,2,2,5]=>11 [1,1,2,5,2]=>11 [1,1,5,2,2]=>11 [1,2,1,2,5]=>11 [1,2,1,5,2]=>11 [1,2,2,1,5]=>11 [1,2,2,5,1]=>11 [1,2,5,1,2]=>11 [1,2,5,2,1]=>11 [1,5,1,2,2]=>11 [1,5,2,1,2]=>11 [1,5,2,2,1]=>11 [2,1,1,2,5]=>11 [2,1,1,5,2]=>11 [2,1,2,1,5]=>11 [2,1,2,5,1]=>11 [2,1,5,1,2]=>11 [2,1,5,2,1]=>11 [2,2,1,1,5]=>11 [2,2,1,5,1]=>11 [2,2,5,1,1]=>11 [2,5,1,1,2]=>11 [2,5,1,2,1]=>11 [2,5,2,1,1]=>11 [5,1,1,2,2]=>11 [5,1,2,1,2]=>11 [5,1,2,2,1]=>11 [5,2,1,1,2]=>11 [5,2,1,2,1]=>11 [5,2,2,1,1]=>11 [1,1,2,3,3]=>10 [1,1,3,2,3]=>10 [1,1,3,3,2]=>10 [1,2,1,3,3]=>10 [1,2,3,1,3]=>10 [1,2,3,3,1]=>10 [1,3,1,2,3]=>10 [1,3,1,3,2]=>10 [1,3,2,1,3]=>10 [1,3,2,3,1]=>10 [1,3,3,1,2]=>10 [1,3,3,2,1]=>10 [2,1,1,3,3]=>10 [2,1,3,1,3]=>10 [2,1,3,3,1]=>10 [2,3,1,1,3]=>10 [2,3,1,3,1]=>10 [2,3,3,1,1]=>10 [3,1,1,2,3]=>10 [3,1,1,3,2]=>10 [3,1,2,1,3]=>10 [3,1,2,3,1]=>10 [3,1,3,1,2]=>10 [3,1,3,2,1]=>10 [3,2,1,1,3]=>10 [3,2,1,3,1]=>10 [3,2,3,1,1]=>10 [3,3,1,1,2]=>10 [3,3,1,2,1]=>10 [3,3,2,1,1]=>10 [1,1,2,3,4]=>11 [1,1,2,4,3]=>11 [1,1,3,2,4]=>11 [1,1,3,4,2]=>11 [1,1,4,2,3]=>11 [1,1,4,3,2]=>11 [1,2,1,3,4]=>11 [1,2,1,4,3]=>11 [1,2,3,1,4]=>11 [1,2,3,4,1]=>11 [1,2,4,1,3]=>11 [1,2,4,3,1]=>11 [1,3,1,2,4]=>11 [1,3,1,4,2]=>11 [1,3,2,1,4]=>11 [1,3,2,4,1]=>11 [1,3,4,1,2]=>11 [1,3,4,2,1]=>11 [1,4,1,2,3]=>11 [1,4,1,3,2]=>11 [1,4,2,1,3]=>11 [1,4,2,3,1]=>11 [1,4,3,1,2]=>11 [1,4,3,2,1]=>11 [2,1,1,3,4]=>11 [2,1,1,4,3]=>11 [2,1,3,1,4]=>11 [2,1,3,4,1]=>11 [2,1,4,1,3]=>11 [2,1,4,3,1]=>11 [2,3,1,1,4]=>11 [2,3,1,4,1]=>11 [2,3,4,1,1]=>11 [2,4,1,1,3]=>11 [2,4,1,3,1]=>11 [2,4,3,1,1]=>11 [3,1,1,2,4]=>11 [3,1,1,4,2]=>11 [3,1,2,1,4]=>11 [3,1,2,4,1]=>11 [3,1,4,1,2]=>11 [3,1,4,2,1]=>11 [3,2,1,1,4]=>11 [3,2,1,4,1]=>11 [3,2,4,1,1]=>11 [3,4,1,1,2]=>11 [3,4,1,2,1]=>11 [3,4,2,1,1]=>11 [4,1,1,2,3]=>11 [4,1,1,3,2]=>11 [4,1,2,1,3]=>11 [4,1,2,3,1]=>11 [4,1,3,1,2]=>11 [4,1,3,2,1]=>11 [4,2,1,1,3]=>11 [4,2,1,3,1]=>11 [4,2,3,1,1]=>11 [4,3,1,1,2]=>11 [4,3,1,2,1]=>11 [4,3,2,1,1]=>11 [1,1,2,3,5]=>12 [1,1,2,5,3]=>12 [1,1,3,2,5]=>12 [1,1,3,5,2]=>12 [1,1,5,2,3]=>12 [1,1,5,3,2]=>12 [1,2,1,3,5]=>12 [1,2,1,5,3]=>12 [1,2,3,1,5]=>12 [1,2,3,5,1]=>12 [1,2,5,1,3]=>12 [1,2,5,3,1]=>12 [1,3,1,2,5]=>12 [1,3,1,5,2]=>12 [1,3,2,1,5]=>12 [1,3,2,5,1]=>12 [1,3,5,1,2]=>12 [1,3,5,2,1]=>12 [1,5,1,2,3]=>12 [1,5,1,3,2]=>12 [1,5,2,1,3]=>12 [1,5,2,3,1]=>12 [1,5,3,1,2]=>12 [1,5,3,2,1]=>12 [2,1,1,3,5]=>12 [2,1,1,5,3]=>12 [2,1,3,1,5]=>12 [2,1,3,5,1]=>12 [2,1,5,1,3]=>12 [2,1,5,3,1]=>12 [2,3,1,1,5]=>12 [2,3,1,5,1]=>12 [2,3,5,1,1]=>12 [2,5,1,1,3]=>12 [2,5,1,3,1]=>12 [2,5,3,1,1]=>12 [3,1,1,2,5]=>12 [3,1,1,5,2]=>12 [3,1,2,1,5]=>12 [3,1,2,5,1]=>12 [3,1,5,1,2]=>12 [3,1,5,2,1]=>12 [3,2,1,1,5]=>12 [3,2,1,5,1]=>12 [3,2,5,1,1]=>12 [3,5,1,1,2]=>12 [3,5,1,2,1]=>12 [3,5,2,1,1]=>12 [5,1,1,2,3]=>12 [5,1,1,3,2]=>12 [5,1,2,1,3]=>12 [5,1,2,3,1]=>12 [5,1,3,1,2]=>12 [5,1,3,2,1]=>12 [5,2,1,1,3]=>12 [5,2,1,3,1]=>12 [5,2,3,1,1]=>12 [5,3,1,1,2]=>12 [5,3,1,2,1]=>12 [5,3,2,1,1]=>12 [1,1,2,4,4]=>12 [1,1,4,2,4]=>12 [1,1,4,4,2]=>12 [1,2,1,4,4]=>12 [1,2,4,1,4]=>12 [1,2,4,4,1]=>12 [1,4,1,2,4]=>12 [1,4,1,4,2]=>12 [1,4,2,1,4]=>12 [1,4,2,4,1]=>12 [1,4,4,1,2]=>12 [1,4,4,2,1]=>12 [2,1,1,4,4]=>12 [2,1,4,1,4]=>12 [2,1,4,4,1]=>12 [2,4,1,1,4]=>12 [2,4,1,4,1]=>12 [2,4,4,1,1]=>12 [4,1,1,2,4]=>12 [4,1,1,4,2]=>12 [4,1,2,1,4]=>12 [4,1,2,4,1]=>12 [4,1,4,1,2]=>12 [4,1,4,2,1]=>12 [4,2,1,1,4]=>12 [4,2,1,4,1]=>12 [4,2,4,1,1]=>12 [4,4,1,1,2]=>12 [4,4,1,2,1]=>12 [4,4,2,1,1]=>12 [1,1,2,4,5]=>13 [1,1,2,5,4]=>13 [1,1,4,2,5]=>13 [1,1,4,5,2]=>13 [1,1,5,2,4]=>13 [1,1,5,4,2]=>13 [1,2,1,4,5]=>13 [1,2,1,5,4]=>13 [1,2,4,1,5]=>13 [1,2,4,5,1]=>13 [1,2,5,1,4]=>13 [1,2,5,4,1]=>13 [1,4,1,2,5]=>13 [1,4,1,5,2]=>13 [1,4,2,1,5]=>13 [1,4,2,5,1]=>13 [1,4,5,1,2]=>13 [1,4,5,2,1]=>13 [1,5,1,2,4]=>13 [1,5,1,4,2]=>13 [1,5,2,1,4]=>13 [1,5,2,4,1]=>13 [1,5,4,1,2]=>13 [1,5,4,2,1]=>13 [2,1,1,4,5]=>13 [2,1,1,5,4]=>13 [2,1,4,1,5]=>13 [2,1,4,5,1]=>13 [2,1,5,1,4]=>13 [2,1,5,4,1]=>13 [2,4,1,1,5]=>13 [2,4,1,5,1]=>13 [2,4,5,1,1]=>13 [2,5,1,1,4]=>13 [2,5,1,4,1]=>13 [2,5,4,1,1]=>13 [4,1,1,2,5]=>13 [4,1,1,5,2]=>13 [4,1,2,1,5]=>13 [4,1,2,5,1]=>13 [4,1,5,1,2]=>13 [4,1,5,2,1]=>13 [4,2,1,1,5]=>13 [4,2,1,5,1]=>13 [4,2,5,1,1]=>13 [4,5,1,1,2]=>13 [4,5,1,2,1]=>13 [4,5,2,1,1]=>13 [5,1,1,2,4]=>13 [5,1,1,4,2]=>13 [5,1,2,1,4]=>13 [5,1,2,4,1]=>13 [5,1,4,1,2]=>13 [5,1,4,2,1]=>13 [5,2,1,1,4]=>13 [5,2,1,4,1]=>13 [5,2,4,1,1]=>13 [5,4,1,1,2]=>13 [5,4,1,2,1]=>13 [5,4,2,1,1]=>13 [1,1,3,3,3]=>11 [1,3,1,3,3]=>11 [1,3,3,1,3]=>11 [1,3,3,3,1]=>11 [3,1,1,3,3]=>11 [3,1,3,1,3]=>11 [3,1,3,3,1]=>11 [3,3,1,1,3]=>11 [3,3,1,3,1]=>11 [3,3,3,1,1]=>11 [1,1,3,3,4]=>12 [1,1,3,4,3]=>12 [1,1,4,3,3]=>12 [1,3,1,3,4]=>12 [1,3,1,4,3]=>12 [1,3,3,1,4]=>12 [1,3,3,4,1]=>12 [1,3,4,1,3]=>12 [1,3,4,3,1]=>12 [1,4,1,3,3]=>12 [1,4,3,1,3]=>12 [1,4,3,3,1]=>12 [3,1,1,3,4]=>12 [3,1,1,4,3]=>12 [3,1,3,1,4]=>12 [3,1,3,4,1]=>12 [3,1,4,1,3]=>12 [3,1,4,3,1]=>12 [3,3,1,1,4]=>12 [3,3,1,4,1]=>12 [3,3,4,1,1]=>12 [3,4,1,1,3]=>12 [3,4,1,3,1]=>12 [3,4,3,1,1]=>12 [4,1,1,3,3]=>12 [4,1,3,1,3]=>12 [4,1,3,3,1]=>12 [4,3,1,1,3]=>12 [4,3,1,3,1]=>12 [4,3,3,1,1]=>12 [1,1,3,3,5]=>13 [1,1,3,5,3]=>13 [1,1,5,3,3]=>13 [1,3,1,3,5]=>13 [1,3,1,5,3]=>13 [1,3,3,1,5]=>13 [1,3,3,5,1]=>13 [1,3,5,1,3]=>13 [1,3,5,3,1]=>13 [1,5,1,3,3]=>13 [1,5,3,1,3]=>13 [1,5,3,3,1]=>13 [3,1,1,3,5]=>13 [3,1,1,5,3]=>13 [3,1,3,1,5]=>13 [3,1,3,5,1]=>13 [3,1,5,1,3]=>13 [3,1,5,3,1]=>13 [3,3,1,1,5]=>13 [3,3,1,5,1]=>13 [3,3,5,1,1]=>13 [3,5,1,1,3]=>13 [3,5,1,3,1]=>13 [3,5,3,1,1]=>13 [5,1,1,3,3]=>13 [5,1,3,1,3]=>13 [5,1,3,3,1]=>13 [5,3,1,1,3]=>13 [5,3,1,3,1]=>13 [5,3,3,1,1]=>13 [1,1,3,4,4]=>13 [1,1,4,3,4]=>13 [1,1,4,4,3]=>13 [1,3,1,4,4]=>13 [1,3,4,1,4]=>13 [1,3,4,4,1]=>13 [1,4,1,3,4]=>13 [1,4,1,4,3]=>13 [1,4,3,1,4]=>13 [1,4,3,4,1]=>13 [1,4,4,1,3]=>13 [1,4,4,3,1]=>13 [3,1,1,4,4]=>13 [3,1,4,1,4]=>13 [3,1,4,4,1]=>13 [3,4,1,1,4]=>13 [3,4,1,4,1]=>13 [3,4,4,1,1]=>13 [4,1,1,3,4]=>13 [4,1,1,4,3]=>13 [4,1,3,1,4]=>13 [4,1,3,4,1]=>13 [4,1,4,1,3]=>13 [4,1,4,3,1]=>13 [4,3,1,1,4]=>13 [4,3,1,4,1]=>13 [4,3,4,1,1]=>13 [4,4,1,1,3]=>13 [4,4,1,3,1]=>13 [4,4,3,1,1]=>13 [1,1,3,4,5]=>14 [1,1,3,5,4]=>14 [1,1,4,3,5]=>14 [1,1,4,5,3]=>14 [1,1,5,3,4]=>14 [1,1,5,4,3]=>14 [1,3,1,4,5]=>14 [1,3,1,5,4]=>14 [1,3,4,1,5]=>14 [1,3,4,5,1]=>14 [1,3,5,1,4]=>14 [1,3,5,4,1]=>14 [1,4,1,3,5]=>14 [1,4,1,5,3]=>14 [1,4,3,1,5]=>14 [1,4,3,5,1]=>14 [1,4,5,1,3]=>14 [1,4,5,3,1]=>14 [1,5,1,3,4]=>14 [1,5,1,4,3]=>14 [1,5,3,1,4]=>14 [1,5,3,4,1]=>14 [1,5,4,1,3]=>14 [1,5,4,3,1]=>14 [3,1,1,4,5]=>14 [3,1,1,5,4]=>14 [3,1,4,1,5]=>14 [3,1,4,5,1]=>14 [3,1,5,1,4]=>14 [3,1,5,4,1]=>14 [3,4,1,1,5]=>14 [3,4,1,5,1]=>14 [3,4,5,1,1]=>14 [3,5,1,1,4]=>14 [3,5,1,4,1]=>14 [3,5,4,1,1]=>14 [4,1,1,3,5]=>14 [4,1,1,5,3]=>14 [4,1,3,1,5]=>14 [4,1,3,5,1]=>14 [4,1,5,1,3]=>14 [4,1,5,3,1]=>14 [4,3,1,1,5]=>14 [4,3,1,5,1]=>14 [4,3,5,1,1]=>14 [4,5,1,1,3]=>14 [4,5,1,3,1]=>14 [4,5,3,1,1]=>14 [5,1,1,3,4]=>14 [5,1,1,4,3]=>14 [5,1,3,1,4]=>14 [5,1,3,4,1]=>14 [5,1,4,1,3]=>14 [5,1,4,3,1]=>14 [5,3,1,1,4]=>14 [5,3,1,4,1]=>14 [5,3,4,1,1]=>14 [5,4,1,1,3]=>14 [5,4,1,3,1]=>14 [5,4,3,1,1]=>14 [1,2,2,2,2]=>9 [2,1,2,2,2]=>9 [2,2,1,2,2]=>9 [2,2,2,1,2]=>9 [2,2,2,2,1]=>9 [1,2,2,2,3]=>10 [1,2,2,3,2]=>10 [1,2,3,2,2]=>10 [1,3,2,2,2]=>10 [2,1,2,2,3]=>10 [2,1,2,3,2]=>10 [2,1,3,2,2]=>10 [2,2,1,2,3]=>10 [2,2,1,3,2]=>10 [2,2,2,1,3]=>10 [2,2,2,3,1]=>10 [2,2,3,1,2]=>10 [2,2,3,2,1]=>10 [2,3,1,2,2]=>10 [2,3,2,1,2]=>10 [2,3,2,2,1]=>10 [3,1,2,2,2]=>10 [3,2,1,2,2]=>10 [3,2,2,1,2]=>10 [3,2,2,2,1]=>10 [1,2,2,2,4]=>11 [1,2,2,4,2]=>11 [1,2,4,2,2]=>11 [1,4,2,2,2]=>11 [2,1,2,2,4]=>11 [2,1,2,4,2]=>11 [2,1,4,2,2]=>11 [2,2,1,2,4]=>11 [2,2,1,4,2]=>11 [2,2,2,1,4]=>11 [2,2,2,4,1]=>11 [2,2,4,1,2]=>11 [2,2,4,2,1]=>11 [2,4,1,2,2]=>11 [2,4,2,1,2]=>11 [2,4,2,2,1]=>11 [4,1,2,2,2]=>11 [4,2,1,2,2]=>11 [4,2,2,1,2]=>11 [4,2,2,2,1]=>11 [1,2,2,2,5]=>12 [1,2,2,5,2]=>12 [1,2,5,2,2]=>12 [1,5,2,2,2]=>12 [2,1,2,2,5]=>12 [2,1,2,5,2]=>12 [2,1,5,2,2]=>12 [2,2,1,2,5]=>12 [2,2,1,5,2]=>12 [2,2,2,1,5]=>12 [2,2,2,5,1]=>12 [2,2,5,1,2]=>12 [2,2,5,2,1]=>12 [2,5,1,2,2]=>12 [2,5,2,1,2]=>12 [2,5,2,2,1]=>12 [5,1,2,2,2]=>12 [5,2,1,2,2]=>12 [5,2,2,1,2]=>12 [5,2,2,2,1]=>12 [1,2,2,3,3]=>11 [1,2,3,2,3]=>11 [1,2,3,3,2]=>11 [1,3,2,2,3]=>11 [1,3,2,3,2]=>11 [1,3,3,2,2]=>11 [2,1,2,3,3]=>11 [2,1,3,2,3]=>11 [2,1,3,3,2]=>11 [2,2,1,3,3]=>11 [2,2,3,1,3]=>11 [2,2,3,3,1]=>11 [2,3,1,2,3]=>11 [2,3,1,3,2]=>11 [2,3,2,1,3]=>11 [2,3,2,3,1]=>11 [2,3,3,1,2]=>11 [2,3,3,2,1]=>11 [3,1,2,2,3]=>11 [3,1,2,3,2]=>11 [3,1,3,2,2]=>11 [3,2,1,2,3]=>11 [3,2,1,3,2]=>11 [3,2,2,1,3]=>11 [3,2,2,3,1]=>11 [3,2,3,1,2]=>11 [3,2,3,2,1]=>11 [3,3,1,2,2]=>11 [3,3,2,1,2]=>11 [3,3,2,2,1]=>11 [1,2,2,3,4]=>12 [1,2,2,4,3]=>12 [1,2,3,2,4]=>12 [1,2,3,4,2]=>12 [1,2,4,2,3]=>12 [1,2,4,3,2]=>12 [1,3,2,2,4]=>12 [1,3,2,4,2]=>12 [1,3,4,2,2]=>12 [1,4,2,2,3]=>12 [1,4,2,3,2]=>12 [1,4,3,2,2]=>12 [2,1,2,3,4]=>12 [2,1,2,4,3]=>12 [2,1,3,2,4]=>12 [2,1,3,4,2]=>12 [2,1,4,2,3]=>12 [2,1,4,3,2]=>12 [2,2,1,3,4]=>12 [2,2,1,4,3]=>12 [2,2,3,1,4]=>12 [2,2,3,4,1]=>12 [2,2,4,1,3]=>12 [2,2,4,3,1]=>12 [2,3,1,2,4]=>12 [2,3,1,4,2]=>12 [2,3,2,1,4]=>12 [2,3,2,4,1]=>12 [2,3,4,1,2]=>12 [2,3,4,2,1]=>12 [2,4,1,2,3]=>12 [2,4,1,3,2]=>12 [2,4,2,1,3]=>12 [2,4,2,3,1]=>12 [2,4,3,1,2]=>12 [2,4,3,2,1]=>12 [3,1,2,2,4]=>12 [3,1,2,4,2]=>12 [3,1,4,2,2]=>12 [3,2,1,2,4]=>12 [3,2,1,4,2]=>12 [3,2,2,1,4]=>12 [3,2,2,4,1]=>12 [3,2,4,1,2]=>12 [3,2,4,2,1]=>12 [3,4,1,2,2]=>12 [3,4,2,1,2]=>12 [3,4,2,2,1]=>12 [4,1,2,2,3]=>12 [4,1,2,3,2]=>12 [4,1,3,2,2]=>12 [4,2,1,2,3]=>12 [4,2,1,3,2]=>12 [4,2,2,1,3]=>12 [4,2,2,3,1]=>12 [4,2,3,1,2]=>12 [4,2,3,2,1]=>12 [4,3,1,2,2]=>12 [4,3,2,1,2]=>12 [4,3,2,2,1]=>12 [1,2,2,3,5]=>13 [1,2,2,5,3]=>13 [1,2,3,2,5]=>13 [1,2,3,5,2]=>13 [1,2,5,2,3]=>13 [1,2,5,3,2]=>13 [1,3,2,2,5]=>13 [1,3,2,5,2]=>13 [1,3,5,2,2]=>13 [1,5,2,2,3]=>13 [1,5,2,3,2]=>13 [1,5,3,2,2]=>13 [2,1,2,3,5]=>13 [2,1,2,5,3]=>13 [2,1,3,2,5]=>13 [2,1,3,5,2]=>13 [2,1,5,2,3]=>13 [2,1,5,3,2]=>13 [2,2,1,3,5]=>13 [2,2,1,5,3]=>13 [2,2,3,1,5]=>13 [2,2,3,5,1]=>13 [2,2,5,1,3]=>13 [2,2,5,3,1]=>13 [2,3,1,2,5]=>13 [2,3,1,5,2]=>13 [2,3,2,1,5]=>13 [2,3,2,5,1]=>13 [2,3,5,1,2]=>13 [2,3,5,2,1]=>13 [2,5,1,2,3]=>13 [2,5,1,3,2]=>13 [2,5,2,1,3]=>13 [2,5,2,3,1]=>13 [2,5,3,1,2]=>13 [2,5,3,2,1]=>13 [3,1,2,2,5]=>13 [3,1,2,5,2]=>13 [3,1,5,2,2]=>13 [3,2,1,2,5]=>13 [3,2,1,5,2]=>13 [3,2,2,1,5]=>13 [3,2,2,5,1]=>13 [3,2,5,1,2]=>13 [3,2,5,2,1]=>13 [3,5,1,2,2]=>13 [3,5,2,1,2]=>13 [3,5,2,2,1]=>13 [5,1,2,2,3]=>13 [5,1,2,3,2]=>13 [5,1,3,2,2]=>13 [5,2,1,2,3]=>13 [5,2,1,3,2]=>13 [5,2,2,1,3]=>13 [5,2,2,3,1]=>13 [5,2,3,1,2]=>13 [5,2,3,2,1]=>13 [5,3,1,2,2]=>13 [5,3,2,1,2]=>13 [5,3,2,2,1]=>13 [1,2,2,4,4]=>13 [1,2,4,2,4]=>13 [1,2,4,4,2]=>13 [1,4,2,2,4]=>13 [1,4,2,4,2]=>13 [1,4,4,2,2]=>13 [2,1,2,4,4]=>13 [2,1,4,2,4]=>13 [2,1,4,4,2]=>13 [2,2,1,4,4]=>13 [2,2,4,1,4]=>13 [2,2,4,4,1]=>13 [2,4,1,2,4]=>13 [2,4,1,4,2]=>13 [2,4,2,1,4]=>13 [2,4,2,4,1]=>13 [2,4,4,1,2]=>13 [2,4,4,2,1]=>13 [4,1,2,2,4]=>13 [4,1,2,4,2]=>13 [4,1,4,2,2]=>13 [4,2,1,2,4]=>13 [4,2,1,4,2]=>13 [4,2,2,1,4]=>13 [4,2,2,4,1]=>13 [4,2,4,1,2]=>13 [4,2,4,2,1]=>13 [4,4,1,2,2]=>13 [4,4,2,1,2]=>13 [4,4,2,2,1]=>13 [1,2,2,4,5]=>14 [1,2,2,5,4]=>14 [1,2,4,2,5]=>14 [1,2,4,5,2]=>14 [1,2,5,2,4]=>14 [1,2,5,4,2]=>14 [1,4,2,2,5]=>14 [1,4,2,5,2]=>14 [1,4,5,2,2]=>14 [1,5,2,2,4]=>14 [1,5,2,4,2]=>14 [1,5,4,2,2]=>14 [2,1,2,4,5]=>14 [2,1,2,5,4]=>14 [2,1,4,2,5]=>14 [2,1,4,5,2]=>14 [2,1,5,2,4]=>14 [2,1,5,4,2]=>14 [2,2,1,4,5]=>14 [2,2,1,5,4]=>14 [2,2,4,1,5]=>14 [2,2,4,5,1]=>14 [2,2,5,1,4]=>14 [2,2,5,4,1]=>14 [2,4,1,2,5]=>14 [2,4,1,5,2]=>14 [2,4,2,1,5]=>14 [2,4,2,5,1]=>14 [2,4,5,1,2]=>14 [2,4,5,2,1]=>14 [2,5,1,2,4]=>14 [2,5,1,4,2]=>14 [2,5,2,1,4]=>14 [2,5,2,4,1]=>14 [2,5,4,1,2]=>14 [2,5,4,2,1]=>14 [4,1,2,2,5]=>14 [4,1,2,5,2]=>14 [4,1,5,2,2]=>14 [4,2,1,2,5]=>14 [4,2,1,5,2]=>14 [4,2,2,1,5]=>14 [4,2,2,5,1]=>14 [4,2,5,1,2]=>14 [4,2,5,2,1]=>14 [4,5,1,2,2]=>14 [4,5,2,1,2]=>14 [4,5,2,2,1]=>14 [5,1,2,2,4]=>14 [5,1,2,4,2]=>14 [5,1,4,2,2]=>14 [5,2,1,2,4]=>14 [5,2,1,4,2]=>14 [5,2,2,1,4]=>14 [5,2,2,4,1]=>14 [5,2,4,1,2]=>14 [5,2,4,2,1]=>14 [5,4,1,2,2]=>14 [5,4,2,1,2]=>14 [5,4,2,2,1]=>14 [1,2,3,3,3]=>12 [1,3,2,3,3]=>12 [1,3,3,2,3]=>12 [1,3,3,3,2]=>12 [2,1,3,3,3]=>12 [2,3,1,3,3]=>12 [2,3,3,1,3]=>12 [2,3,3,3,1]=>12 [3,1,2,3,3]=>12 [3,1,3,2,3]=>12 [3,1,3,3,2]=>12 [3,2,1,3,3]=>12 [3,2,3,1,3]=>12 [3,2,3,3,1]=>12 [3,3,1,2,3]=>12 [3,3,1,3,2]=>12 [3,3,2,1,3]=>12 [3,3,2,3,1]=>12 [3,3,3,1,2]=>12 [3,3,3,2,1]=>12 [1,2,3,3,4]=>13 [1,2,3,4,3]=>13 [1,2,4,3,3]=>13 [1,3,2,3,4]=>13 [1,3,2,4,3]=>13 [1,3,3,2,4]=>13 [1,3,3,4,2]=>13 [1,3,4,2,3]=>13 [1,3,4,3,2]=>13 [1,4,2,3,3]=>13 [1,4,3,2,3]=>13 [1,4,3,3,2]=>13 [2,1,3,3,4]=>13 [2,1,3,4,3]=>13 [2,1,4,3,3]=>13 [2,3,1,3,4]=>13 [2,3,1,4,3]=>13 [2,3,3,1,4]=>13 [2,3,3,4,1]=>13 [2,3,4,1,3]=>13 [2,3,4,3,1]=>13 [2,4,1,3,3]=>13 [2,4,3,1,3]=>13 [2,4,3,3,1]=>13 [3,1,2,3,4]=>13 [3,1,2,4,3]=>13 [3,1,3,2,4]=>13 [3,1,3,4,2]=>13 [3,1,4,2,3]=>13 [3,1,4,3,2]=>13 [3,2,1,3,4]=>13 [3,2,1,4,3]=>13 [3,2,3,1,4]=>13 [3,2,3,4,1]=>13 [3,2,4,1,3]=>13 [3,2,4,3,1]=>13 [3,3,1,2,4]=>13 [3,3,1,4,2]=>13 [3,3,2,1,4]=>13 [3,3,2,4,1]=>13 [3,3,4,1,2]=>13 [3,3,4,2,1]=>13 [3,4,1,2,3]=>13 [3,4,1,3,2]=>13 [3,4,2,1,3]=>13 [3,4,2,3,1]=>13 [3,4,3,1,2]=>13 [3,4,3,2,1]=>13 [4,1,2,3,3]=>13 [4,1,3,2,3]=>13 [4,1,3,3,2]=>13 [4,2,1,3,3]=>13 [4,2,3,1,3]=>13 [4,2,3,3,1]=>13 [4,3,1,2,3]=>13 [4,3,1,3,2]=>13 [4,3,2,1,3]=>13 [4,3,2,3,1]=>13 []=>0
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Description
The sum of the entries of a parking function.
The generating function for parking functions by sum is the evaluation at $x=1$ and $y=1/q$ of the Tutte polynomial of the complete graph, multiplied by $q^\binom{n}{2}$.
References
[1] Merino López, C. Chip firing and the Tutte polynomial MathSciNet:1630779
Code
def statistic(p):
    return sum(p)

def generating_function(n):
    R. = ZZ[]
    return graphs.CompleteGraph(n).tutte_polynomial().subs(x=1, y=1/q)*q^binomial(n, 2)
Created
Nov 05, 2013 at 18:44 by Jeremy L. Martin
Updated
Mar 27, 2024 at 13:49 by Martin Rubey