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%I #4 Apr 16 2015 19:16:12
%S 512,2848,2848,13504,16677,13504,62579,96680,101227,62579,281213,
%T 541896,732482,594229,281213,1223367,3009795,5352986,5449304,3374539,
%U 1223367,5203324,16759085,40203005,51899365,39971674,19028310,5203324,21804750
%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock sum of the two medians of the central row and column minus the sum of the minimums of the diagonal and antidiagonal nondecreasing horizontally, vertically and ne-to-sw antidiagonally
%C Table starts
%C ......512......2848.......13504........62579.........281213.........1223367
%C .....2848.....16677.......96680.......541896........3009795........16759085
%C ....13504....101227......732482......5352986.......40203005.......303570406
%C ....62579....594229.....5449304.....51899365......519390250......5227360394
%C ...281213...3374539....39971674....502447661.....6713096472.....90781754582
%C ..1223367..19028310...295114929...4926932828....88719570970...1618913713517
%C ..5203324.106805258..2183417807..48470017991..1174259463543..28823946919854
%C .21804750.596053900.16144616160.476479552209.15502395045146.511817645366610
%H R. H. Hardin, <a href="/A257154/b257154.txt">Table of n, a(n) for n = 1..196</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 16] for n>20
%F k=2: [order 44] for n>50
%F k=3: [order 79] for n>87
%F Empirical for row n:
%F n=1: [linear recurrence of order 16] for n>20
%F n=2: [order 57] for n>62
%e Some solutions for n=2 k=4
%e ..0..1..0..0..1..0....0..1..0..0..1..0....0..1..0..1..0..1....0..0..0..0..0..1
%e ..1..0..0..0..0..1....0..0..0..0..0..1....1..0..0..0..1..0....0..0..0..0..0..1
%e ..1..0..0..0..0..1....1..0..0..0..0..1....1..0..0..0..1..1....1..0..0..0..1..0
%e ..0..1..1..0..1..0....0..0..1..1..1..1....1..1..1..1..1..1....1..1..1..0..0..1
%Y Column 1 and row 1 are A254736
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Apr 16 2015
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