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%I #6 Mar 15 2023 11:50:57
%S 0,0,0,0,6,0,0,22,22,0,0,200,328,200,0,0,1732,8696,8696,1732,0,0,
%T 14384,220970,741638,220970,14384,0,0,121696,5669980,66622532,
%U 66622532,5669980,121696,0,0,1027464,145756934,5943688666,20816992724,5943688666
%N T(n,k) = Number of n X k 0..3 arrays x(i,j) with each element horizontally, vertically, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, and upper left element zero.
%C Table starts
%C .0.......0..........0..............0................0................0
%C .0.......6.........22............200.............1732............14384
%C .0......22........328...........8696...........220970..........5669980
%C .0.....200.......8696.........741638.........66622532.......5943688666
%C .0....1732.....220970.......66622532......20816992724....6479894318198
%C .0...14384....5669980.....5943688666....6479894318198.6999441442491276
%C .0..121696..145756934...529115404280.2012129115093308
%C .0.1027464.3741811720.47219421549032
%H R. H. Hardin, <a href="/A230968/b230968.txt">Table of n, a(n) for n = 1..71</a>
%F Empirical for column k:
%F k=2: [linear recurrence order 8]
%F k=3: [order 37]
%e Some solutions for n=3, k=4
%e ..0..1..2..2....0..3..1..0....0..0..0..0....0..2..0..1....0..2..3..1
%e ..1..3..3..1....1..2..3..0....1..3..3..1....3..1..3..2....1..3..0..2
%e ..0..2..2..0....3..0..1..2....0..2..0..2....2..0..0..1....0..2..2..1
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Nov 02 2013