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A238255 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with 2X2 subblock sums lexicographically nondecreasing columnwise and rowwise.

%I A238255 #6 Jul 23 2025 10:49:36
%S A238255 16,44,44,121,180,121,286,804,804,286,676,2818,6828,2818,676,1482,
%T A238255 9991,43456,43456,9991,1482,3249,29995,284992,523578,284992,29995,
%U A238255 3249,6840,90225,1473792,6683137,6683137,1473792,90225,6840,14400,241945,7616082
%N A238255 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with 2X2 subblock sums lexicographically nondecreasing columnwise and rowwise.
%C A238255 Table starts
%C A238255 ....16......44.......121..........286.............676.............1482
%C A238255 ....44.....180.......804.........2818............9991............29995
%C A238255 ...121.....804......6828........43456..........284992..........1473792
%C A238255 ...286....2818.....43456.......523578.........6683137.........65450601
%C A238255 ...676....9991....284992......6683137.......171041320.......3320993180
%C A238255 ..1482...29995...1473792.....65450601......3320993180.....128727296869
%C A238255 ..3249...90225...7616082....640472606.....64353451945....5017308028639
%C A238255 ..6840..241945..32986844...5080416791....992794904591..154350327958339
%C A238255 .14400..649320.142361644..40066932588..15160526139045.4704917436206270
%C A238255 .29640.1605951.537301496.267891545518.192941078342371
%H A238255 R. H. Hardin, <a href="/A238255/b238255.txt">Table of n, a(n) for n = 1..112</a>
%F A238255 Empirical for column k:
%F A238255 k=1: a(n) = 4*a(n-1) -18*a(n-3) +17*a(n-4) +22*a(n-5) -36*a(n-6) +20*a(n-8) -8*a(n-9)
%F A238255 k=2: [order 33]
%F A238255 k=3: [order 81]
%e A238255 Some solutions for n=3 k=4
%e A238255 ..0..0..0..0..1....0..0..0..1..1....0..0..0..1..0....1..0..1..0..1
%e A238255 ..0..0..0..1..1....1..0..1..0..1....0..0..0..0..1....0..0..1..0..1
%e A238255 ..1..1..1..1..0....0..1..0..1..1....0..1..0..0..0....1..1..0..1..0
%e A238255 ..0..0..1..0..1....1..1..1..0..0....1..1..1..1..0....1..0..0..0..1
%Y A238255 Column 1 is A204032
%K A238255 nonn,tabl
%O A238255 1,1
%A A238255 _R. H. Hardin_, Feb 21 2014