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A280227 Number of n X 2 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 A280227 #8 Feb 13 2019 08:05:14
%S A280227 0,4,6,8,14,24,42,72,124,212,362,616,1046,1772,2996,5056,8518,14328,
%T A280227 24066,40368,67628,113164,189154,315848,526894,878164,1462372,2433272,
%U A280227 4045694,6721752,11160282,18517656,30706396,50888132,84287066,139531816
%N A280227 Number of n X 2 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 A280227 R. H. Hardin, <a href="/A280227/b280227.txt">Table of n, a(n) for n = 1..210</a>
%F A280227 Empirical: a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4) for n>7.
%F A280227 Empirical g.f.: x^2*(1 - x)*(1 + x)*(2 - x - 2*x^2 - x^3) / (1 - x - x^2)^2. - _Colin Barker_, Feb 13 2019
%e A280227 All solutions for n=4:
%e A280227 ..0..0. .0..1. .0..0. .0..0. .0..0. .0..0. .0..1. .0..0
%e A280227 ..0..1. .1..1. .0..0. .0..0. .0..0. .1..0. .0..0. .0..0
%e A280227 ..0..0. .1..1. .0..1. .1..0. .0..0. .0..0. .0..0. .0..0
%e A280227 ..0..0. .1..1. .0..0. .0..0. .1..0. .0..0. .0..0. .0..1
%Y A280227 Column 2 of A280233.
%K A280227 nonn
%O A280227 1,2
%A A280227 _R. H. Hardin_, Dec 29 2016