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Regular tetrangle where T(n,k,i) is the number of nonnegative integer matrices up to row and column permutations with no zero rows or columns and k nonzero entries summing to n, with i columns.
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%I #8 Nov 09 2018 21:49:23

%S 1,0,0,1,0,0,1,0,1,2,0,0,1,0,1,2,0,1,2,3,0,0,1,0,2,4,0,1,5,4,0,1,5,5,

%T 5,0,0,1,0,2,4,0,2,10,8,0,1,9,13,7,0,1,5,12,9,7,0,0,1,0,3,6,0,3,16,12,

%U 0,2,24,33,16,0,1,14,36,29,12,0,1,9,23,29

%N Regular tetrangle where T(n,k,i) is the number of nonnegative integer matrices up to row and column permutations with no zero rows or columns and k nonzero entries summing to n, with i columns.

%e Tetrangle begins:

%e 1 0 0 0 0 0

%e 0 1 0 1 0 1 0 1 0 1

%e 0 1 2 0 1 2 0 2 4 0 2 4

%e 0 1 2 3 0 1 5 4 0 2 10 8

%e 0 1 5 5 5 0 1 9 13 7

%e 0 1 5 12 9 7

%Y Triangle sums are A007716. Triangle of row sums is A320801. Triangle of column sums is A317533. Triangle of last columns (without its leading column 1,0,0,0,...) is A055884.

%Y Cf. A000219, A008284, A316980, A316983, A318805, A319616, A320796, A321194.

%K nonn,tabf

%O 1,10

%A _Gus Wiseman_, Nov 09 2018.