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A253294 T(n,k) = Number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock sum differing from its neighbors horizontally, vertically, diagonally and antidiagonally.

%I A253294 #6 Apr 22 2021 14:18:08
%S A253294 81,558,558,3844,3600,3844,26784,23546,23546,26784,186624,167832,
%T A253294 140536,167832,186624,1296000,1184928,1029888,1029888,1184928,1296000,
%U A253294 9000000,8243488,7431136,8153960,7431136,8243488,9000000,62568000,57474376
%N A253294 T(n,k) = Number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock sum differing from its neighbors horizontally, vertically, diagonally and antidiagonally.
%C A253294 Table starts
%C A253294 .........81.........558.........3844........26784.......186624......1296000
%C A253294 ........558........3600........23546.......167832......1184928......8243488
%C A253294 .......3844.......23546.......140536......1029888......7431136.....52784020
%C A253294 ......26784......167832......1029888......8153960.....61286116....465921688
%C A253294 .....186624.....1184928......7431136.....61286116....486417836...4028778100
%C A253294 ....1296000.....8243488.....52784020....465921688...4028778100..36312321352
%C A253294 ....9000000....57474376....376392916...3524494796..32585471254.317292582684
%C A253294 ...62568000...402165016...2705942488..26879615668.268974784168
%C A253294 ..434972736..2811886280..19441124904.204459584768
%C A253294 .3022785216.19648735840.139538118106
%H A253294 R. H. Hardin, <a href="/A253294/b253294.txt">Table of n, a(n) for n = 1..84</a>
%F A253294 Empirical for column k:
%F A253294 k=1: [linear recurrence of order 9];
%F A253294 k=2: [order 40].
%e A253294 Some solutions for n=3, k=4
%e A253294 ..0..0..0..0..2....0..0..0..1..0....0..0..1..2..2....0..0..0..1..2
%e A253294 ..2..0..0..2..1....0..2..2..2..0....0..2..1..2..1....0..0..1..2..2
%e A253294 ..1..0..1..1..2....0..1..2..2..0....2..2..0..0..1....2..0..2..0..2
%e A253294 ..2..1..0..1..1....0..1..1..1..0....1..2..0..2..2....1..2..0..0..1
%Y A253294 Column 1 is A185771.
%K A253294 nonn,tabl
%O A253294 1,1
%A A253294 _R. H. Hardin_, Dec 29 2014