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A224123 T(n,k)=Number of nXk 0..3 arrays with row sums nondecreasing and column sums unimodal.

%I A224123 #6 Jul 23 2025 05:00:07
%S A224123 4,16,10,50,150,20,130,1747,1080,35,296,16782,47059,6627,56,610,
%T A224123 140210,1703178,1070499,36552,84,1163,1050460,53355889,145901795,
%U A224123 21632718,187000,120,2083,7227405,1491827492,17292618579,11066001160,400993828
%N A224123 T(n,k)=Number of nXk 0..3 arrays with row sums nondecreasing and column sums unimodal.
%C A224123 Table starts
%C A224123 ...4......16.........50..........130...........296...........610
%C A224123 ..10.....150.......1747........16782........140210.......1050460
%C A224123 ..20....1080......47059......1703178......53355889....1491827492
%C A224123 ..35....6627....1070499....145901795...17292618579.1830213565657
%C A224123 ..56...36552...21632718..11066001160.4964366292229
%C A224123 ..84..187000..400993828.766386005577
%C A224123 .120..905440.6962188526
%C A224123 .165.4206453
%C A224123 .220
%H A224123 R. H. Hardin, <a href="/A224123/b224123.txt">Table of n, a(n) for n = 1..49</a>
%e A224123 Some solutions for n=3 k=4
%e A224123 ..0..2..2..0....2..0..0..1....2..2..0..0....0..2..3..0....0..0..2..1
%e A224123 ..2..2..2..1....2..2..2..0....2..3..1..0....2..0..3..0....0..0..0..3
%e A224123 ..2..3..1..3....0..2..2..3....0..2..2..3....0..3..2..0....0..1..3..3
%Y A224123 Column 1 is A000292(n+1)
%Y A224123 Column 2 is A223069
%Y A224123 Row 1 is A223659
%K A224123 nonn,tabl
%O A224123 1,1
%A A224123 _R. H. Hardin_ Mar 31 2013