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Number of n X 2 0..2 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.
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%I #9 Feb 12 2019 09:24:31

%S 0,4,6,8,18,36,78,160,338,700,1462,3032,6298,13044,27006,55824,115298,

%T 237868,490310,1009736,2077738,4271972,8776974,18019968,36972018,

%U 75808156,155344598,318145720,651204538,1332235220,2724122782,5567550192

%N Number of n X 2 0..2 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 R. H. Hardin, <a href="/A279896/b279896.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4) for n>7.

%F Empirical g.f.: 2*x^2*(1 - 2*x^2)*(2 - x - 4*x^2 - 2*x^3) / ((1 + x)^2*(1 - 2*x)^2). - _Colin Barker_, Feb 12 2019

%e All solutions for n=4:

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

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

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

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

%Y Column 2 of A279902.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 22 2016