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Number of n X 3 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero.
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%I #10 Feb 09 2018 10:57:36

%S 0,0,10,32,278,2988,23058,199272,1722118,14609220,124974458,

%T 1068235680,9122055726,77940647452,665873921154,5688536171256,

%U 48598714312182,415188274268468,3547028395905802,30302970815445712,258884133806216126

%N Number of n X 3 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero.

%C Column 3 of A231037.

%H R. H. Hardin, <a href="/A231032/b231032.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) -a(n-2) +15*a(n-3) -374*a(n-4) +260*a(n-5) +256*a(n-6) +60*a(n-7) -176*a(n-8) -32*a(n-9).

%F Empirical g.f.: 2*x^3*(5 - 29*x + 184*x^3 - 148*x^4 - 32*x^5) / (1 - 9*x + x^2 - 15*x^3 + 374*x^4 - 260*x^5 - 256*x^6 - 60*x^7 + 176*x^8 + 32*x^9). - _Colin Barker_, Feb 09 2018

%e Some solutions for n=3:

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

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

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

%K nonn

%O 1,3

%A _R. H. Hardin_, Nov 03 2013