Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Feb 09 2018 11:08:43
%S 0,14,50,410,2430,16198,103042,667690,4294910,27706854,178536322,
%T 1150960010,7418522110,47819461126,308233683970,1986827617770,
%U 12806735485950,82550064227622,532103488349058,3429848277235530
%N Number of n X 3 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 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero.
%C Column 3 of A231049.
%H R. H. Hardin, <a href="/A231044/b231044.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +19*a(n-2) +19*a(n-3) +12*a(n-4) -8*a(n-5) +8*a(n-6).
%F Empirical g.f.: 2*x^2*(1 - x)*(7 + 11*x + 8*x^2) / (1 - 3*x - 19*x^2 - 19*x^3 - 12*x^4 + 8*x^5 - 8*x^6). - _Colin Barker_, Feb 09 2018
%e Some solutions for n=4:
%e ..0..3..0....0..1..0....0..1..0....0..1..2....0..1..2....0..1..2....0..1..2
%e ..2..1..0....2..3..2....0..3..2....0..3..2....0..3..0....2..3..2....0..3..2
%e ..2..1..2....2..1..0....2..3..0....2..3..0....0..3..0....1..0..1....0..3..2
%e ..0..3..0....2..3..2....2..1..2....0..1..2....0..1..2....3..2..3....2..1..2
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 03 2013