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%I #4 Jan 21 2014 13:03:01
%S 81,432,432,2304,5805,2304,9504,87450,87450,9504,39204,901317,4297035,
%T 901317,39204,138402,9293996,134940646,134940646,9293996,138402,
%U 488601,73777097,4211459815,13055877546,4211459815,73777097,488601,1553877
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with 2X2 subblock sum of squares lexicographically nondecreasing rowwise and columnwise
%C Table starts
%C .......81.........432...........2304.............9504.............39204
%C ......432........5805..........87450...........901317...........9293996
%C .....2304.......87450........4297035........134940646........4211459815
%C .....9504......901317......134940646......13055877546.....1257559565027
%C ....39204.....9293996.....4211459815....1257559565027...374969850504444
%C ...138402....73777097....95929739101...86958471603770.79511653034814238
%C ...488601...583531732..2162880693927.5933159964415314
%C ..1553877..3814287681.38763321249354
%C ..4941729.24858329516
%C .14587326
%H R. H. Hardin, <a href="/A236282/b236282.txt">Table of n, a(n) for n = 1..60</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 26]
%e Some solutions for n=2 k=4
%e ..0..2..2..0..2....1..2..0..0..2....0..1..2..0..0....0..0..0..0..2
%e ..0..0..0..2..2....1..0..2..2..1....1..0..0..2..2....0..0..2..1..1
%e ..1..2..1..0..0....1..2..1..1..2....2..2..2..1..2....2..1..2..1..2
%Y Column 1 is A235417
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 21 2014