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A280228 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%I A280228 #7 Feb 13 2019 09:25:30
%S A280228 2,6,9,16,29,52,95,168,298,522,911,1580,2729,4694,8046,13748,23425,
%T A280228 39812,67507,114228,192914,325230,547411,919996,1544029,2588002,
%U A280228 4332630,7245208,12103013,20197972,33675911,56098560,93374074,155296914
%N A280228 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%H A280228 R. H. Hardin, <a href="/A280228/b280228.txt">Table of n, a(n) for n = 1..210</a>
%F A280228 Empirical: a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4) for n>7.
%F A280228 Empirical g.f.: x*(2 + 2*x - 5*x^2 - 4*x^3 + 2*x^4 + 2*x^5 + 3*x^6) / (1 - x - x^2)^2. - _Colin Barker_, Feb 13 2019
%e A280228 Some solutions for n=4:
%e A280228 ..0..1..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..1..1
%e A280228 ..0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .1..1..1
%e A280228 ..0..0..0. .1..1..0. .0..1..0. .0..0..0. .0..0..0. .0..1..1. .1..1..1
%e A280228 ..0..0..0. .1..1..1. .0..0..0. .1..0..0. .0..0..1. .1..1..1. .1..1..1
%Y A280228 Column 3 of A280233.
%K A280228 nonn
%O A280228 1,1
%A A280228 _R. H. Hardin_, Dec 29 2016