A253164 - OEIS

%I #4 Dec 28 2014 08:25:00

%S 81,558,558,3844,5136,3844,26784,46752,46752,26784,186624,443362,

%T 555842,443362,186624,1296000,4189216,7252320,7252320,4189216,1296000,

%U 9000000,39478862,92998506,135741428,92998506,39478862,9000000,62568000

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock sum differing from its neighbors horizontally, vertically and nw-se diagonally

%C Table starts

%C .........81.........558.........3844........26784........186624.......1296000

%C ........558........5136........46752.......443362.......4189216......39478862

%C .......3844.......46752.......555842......7252320......92998506....1190692584

%C ......26784......443362......7252320....135741428....2461955138...44789509812

%C .....186624.....4189216.....92998506...2461955138...62954425188.1612778665632

%C ....1296000....39478862...1190692584..44789509812.1612778665632

%C ....9000000...371551030..15179218714.808045500430

%C ...62568000..3500351616.194198939906

%C ..434972736.32968666098

%C .3022785216

%H R. H. Hardin, <a href="/A253164/b253164.txt">Table of n, a(n) for n = 1..60</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) +96*a(n-3) +504*a(n-4) +792*a(n-5) +2304*a(n-6) -13824*a(n-8) -13824*a(n-9)

%e Some solutions for n=2 k=4

%e ..0..2..1..2..2....0..0..0..1..1....0..0..1..1..2....0..0..1..0..0

%e ..0..2..2..0..0....0..1..2..2..0....1..2..1..2..1....0..2..1..1..1

%e ..1..0..1..1..0....2..0..2..0..0....1..0..2..1..0....1..2..2..2..1

%Y Column 1 is A185771

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 28 2014