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%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
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