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Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
1

%I #7 Feb 10 2019 12:38:49

%S 2,10,29,86,240,626,1603,4030,9973,24388,59068,141920,338689,803630,

%T 1897359,4460226,10444904,24376990,56720671,131619998,304674313,

%U 703690416,1621976820,3731637260,8570604669,19653441614,45002040707

%N Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A279263/b279263.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-3) - 4*a(n-4) - a(n-6) for n>9.

%F Empirical g.f.: x*(2 + 2*x - 3*x^2 + 6*x^3 - 8*x^5 + 5*x^6 - 4*x^7 + 2*x^8) / (1 - 2*x - x^3)^2. - _Colin Barker_, Feb 10 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 3 of A279268.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 08 2016