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A229870 T(n,k)=Number of n X n 0..k arrays with corresponding row and column sums equal.

%I A229870 #7 Jul 23 2025 05:48:19
%S A229870 2,3,8,4,27,80,5,64,1215,2432,6,125,8704,384183,247552,7,216,40625,
%T A229870 15106048,923742873,88060928,8,343,143856,266515625,354003288064,
%U A229870 17451302074317,112371410944,9,512,420175,2805425280,36821326171875
%N A229870 T(n,k)=Number of n X n 0..k arrays with corresponding row and column sums equal.
%C A229870 Table starts
%C A229870 ......2.........3............4..............5................6...........7
%C A229870 ......8........27...........64............125..............216.........343
%C A229870 .....80......1215.........8704..........40625...........143856......420175
%C A229870 ...2432....384183.....15106048......266515625.......2805425280.20610104767
%C A229870 .247552.923742873.354003288064.36821326171875.1656812779036416
%H A229870 R. H. Hardin, <a href="/A229870/b229870.txt">Table of n, a(n) for n = 1..43</a>
%F A229870 Empirical for row n:
%F A229870 n=1: a(n) = n + 1
%F A229870 n=2: a(n) = n^3 + 3*n^2 + 3*n + 1
%F A229870 n=3: [polynomial of degree 7]
%F A229870 n=4: [polynomial of degree 13]
%e A229870 Some solutions for n=4 k=4
%e A229870 ..0..0..0..1....0..0..0..1....0..0..0..0....0..0..1..1....0..0..1..1
%e A229870 ..0..1..2..1....0..0..3..4....0..0..3..3....0..1..0..3....0..0..2..2
%e A229870 ..1..0..0..3....1..4..2..0....0..4..0..2....1..3..4..0....1..3..4..1
%e A229870 ..0..3..2..1....0..3..2..2....0..2..3..2....1..0..3..2....1..1..2..0
%Y A229870 Row 2 is A000578(n+1)
%Y A229870 Row 3 is A168364(n+1)
%K A229870 nonn,tabl
%O A229870 1,1
%A A229870 _R. H. Hardin_, Oct 01 2013