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A275229 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

%I A275229 #7 Feb 02 2019 10:46:56
%S A275229 2,11,61,339,1885,10483,58301,324243,1803293,10029107,55777405,
%T A275229 310208979,1725243613,9595033459,53363285309,296782729491,
%U A275229 1650572823965,9179747931827,51053652931069,283937587062867,1579133885991517
%N A275229 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.
%H A275229 R. H. Hardin, <a href="/A275229/b275229.txt">Table of n, a(n) for n = 1..210</a>
%F A275229 Empirical: a(n) = 7*a(n-1) - 8*a(n-2).
%F A275229 Conjectures from _Colin Barker_, Feb 02 2019: (Start)
%F A275229 G.f.: x*(2 - 3*x) / (1 - 7*x + 8*x^2).
%F A275229 a(n) = (2^(-4-n) * ((7-sqrt(17))^n * (-11+3*sqrt(17)) + (7+sqrt(17))^n*(11+3*sqrt(17)))) / sqrt(17).
%F A275229 (End)
%e A275229 Some solutions for n=4:
%e A275229 ..0..1..1..0. .0..1..1..1. .0..1..0..1. .0..0..0..0. .0..1..2..1
%e A275229 ..2..0..0..1. .1..0..2..2. .2..0..1..0. .1..2..1..1. .1..0..1..0
%e A275229 ..0..2..2..2. .2..2..0..0. .0..1..0..2. .2..1..2..2. .2..1..2..1
%Y A275229 Row 3 of A275228.
%K A275229 nonn
%O A275229 1,1
%A A275229 _R. H. Hardin_, Jul 20 2016