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T(n,k)=Number of (n+3)X(k+3) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero
9

%I #4 Oct 30 2013 06:36:52

%S 144,1024,1024,23104,32912,23104,394384,2096704,2096704,394384,

%T 5475600,84019184,280495504,84019184,5475600,84052224,3164737536,

%U 29033433664,29033433664,3164737536,84052224,1326125056,128788339184,2918671561744

%N T(n,k)=Number of (n+3)X(k+3) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero

%C Table starts

%C ......144.........1024...........23104.............394384...............5475600

%C .....1024........32912.........2096704...........84019184............3164737536

%C ....23104......2096704.......280495504........29033433664.........2918671561744

%C ...394384.....84019184.....29033433664......7664693723264......1994194775462464

%C ..5475600...3164737536...2918671561744...1994194775462464...1365596520787459216

%C .84052224.128788339184.312443804166400.556151445605511168.991594953505024518400

%H R. H. Hardin, <a href="/A230796/b230796.txt">Table of n, a(n) for n = 1..111</a>

%F Empirical for column k:

%F k=1: [order 15]

%F k=2: [order 64]

%e Some solutions for n=1 k=4

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

%e ..0..1..2..1..3..1..1....3..1..1..3..1..1..3....3..1..1..3..1..1..3

%e ..2..1..0..3..2..2..0....0..2..2..0..0..0..2....0..0..2..2..0..0..2

%e ..0..3..0..3..2..1..1....1..1..3..3..3..3..3....3..3..1..1..3..3..3

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Oct 30 2013