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%I #6 Apr 11 2022 18:24:17
%S 256,2272,2272,20164,61080,20164,131208,1693053,1649707,131208,853776,
%T 33809449,136233789,32516127,853776,4548852,677462696,8689553076,
%U 8849747316,636820654,4548852,24235929,10650729023,540301382239
%N T(n,k) = Number of (n+1) X (k+1) 0..3 arrays with 2 X 2 subblock sum of squares lexicographically nondecreasing rowwise and nonincreasing columnwise.
%C Table starts
%C .......256..........2272............20164............131208.............853776
%C ......2272.........61080..........1693053..........33809449..........677462696
%C .....20164.......1649707........136233789........8689553076.......540301382239
%C ....131208......32516127.......8849747316.....2001758743204....439572860964268
%C ....853776.....636820654.....569055271070...448691506243509.339098156459115852
%C ...4548852....9861273365...29822537207178.85371358783135523
%C ..24235929..152479393753.1571264979362306
%C .112067172.1957874677935
%C .518199696
%H R. H. Hardin, <a href="/A235521/b235521.txt">Table of n, a(n) for n = 1..49</a>
%F Empirical for column and row 1: [linear recurrence of order 50].
%e Some solutions for n=2, k=4
%e ..0..2..0..1..0....0..0..0..0..0....0..2..0..0..0....0..2..0..0..1
%e ..1..2..1..1..1....1..3..0..1..0....1..1..1..0..0....1..1..1..1..0
%e ..2..3..1..3..0....0..2..3..1..1....3..2..2..3..3....3..0..2..2..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 11 2014
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