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A277761 Number of n X 2 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

%I A277761 #9 Feb 05 2019 18:42:42
%S A277761 0,1,2,14,56,284,1304,6248,29408,139472,659360,3121376,14768000,
%T A277761 69887936,330703232,1564924544,7405262336,35042157824,165821110784,
%U A277761 784674242048,3713117739008,17570663078912,83145267845120,393447636985856
%N A277761 Number of n X 2 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.
%H A277761 R. H. Hardin, <a href="/A277761/b277761.txt">Table of n, a(n) for n = 1..210</a>
%F A277761 Empirical: a(n) = 4*a(n-1) + 6*a(n-2) - 12*a(n-3).
%F A277761 Conjectures from _Colin Barker_, Feb 05 2019: (Start)
%F A277761 G.f.: x^2*(1 - 2*x) / ((1 + 2*x)*(1 - 6*x + 6*x^2)).
%F A277761 a(n) = (3*(-1)^n*2^(2+n) - (-5+sqrt(3))*(3+sqrt(3))^n + (3-sqrt(3))^n*(5+sqrt(3))) / 132.
%F A277761 (End)
%e A277761 Some solutions for n=4:
%e A277761 ..0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..1
%e A277761 ..2..2. .2..2. .2..2. .2..2. .2..2. .2..2. .2..2. .2..2. .2..2. .2..2
%e A277761 ..2..0. .0..1. .1..2. .0..1. .1..0. .0..1. .0..1. .2..1. .1..0. .1..0
%e A277761 ..1..1. .2..2. .0..0. .2..0. .0..2. .1..2. .2..1. .0..0. .1..2. .2..2
%Y A277761 Column 2 of A277767.
%K A277761 nonn
%O A277761 1,3
%A A277761 _R. H. Hardin_, Oct 29 2016