%I #8 Sep 28 2018 06:54:45
%S 0,6,78,464,3090,22460,162766,1169472,8396770,60331460,433549110,
%T 3115381720,22385974490,160857679996,1155868628526,8305679220784,
%U 59681777605042,428852885779252,3081590524869798,22143258241832392
%N Number of 3 X n 0..3 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
%H R. H. Hardin, <a href="/A231248/b231248.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 7*a(n-1) - 3*a(n-2) + 27*a(n-3) + 28*a(n-4) + 14*a(n-5) - 8*a(n-6) - 8*a(n-7) for n>8.
%F Empirical g.f.: 2*x^2*(3 + 18*x - 32*x^2 - 43*x^3 - 26*x^4 + 10*x^5 + 12*x^6) / (1 - 7*x + 3*x^2 - 27*x^3 - 28*x^4 - 14*x^5 + 8*x^6 + 8*x^7). - _Colin Barker_, Sep 28 2018
%e Some solutions for n=4:
%e ..0..1..0..1....0..3..2..1....0..3..2..1....0..1..2..1....0..3..0..3
%e ..2..3..2..1....0..1..0..1....2..1..0..1....2..3..2..3....2..1..2..1
%e ..0..1..0..3....2..3..2..1....0..3..2..3....0..1..0..1....0..1..0..3
%Y Row 3 of A231246.
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 06 2013