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A279736 Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%I A279736 #8 Feb 11 2019 14:23:06
%S A279736 2,6,35,168,766,3402,14827,63680,270313,1136546,4740986,19644984,
%T A279736 80939021,331835984,1354628539,5508982340,22328647462,90229615030,
%U A279736 363633214831,1461903606752,5864244756909,23476219277174,93808204087890
%N A279736 Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%H A279736 R. H. Hardin, <a href="/A279736/b279736.txt">Table of n, a(n) for n = 1..210</a>
%F A279736 Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 54*a(n-3) - 45*a(n-4) + 20*a(n-5) - 4*a(n-6) for n>7.
%F A279736 Empirical g.f.: x*(1 - x)*(1 - 2*x)*(2 - 8*x + 17*x^2 - 13*x^3 + 4*x^4) / (1 - 5*x + 5*x^2 - 2*x^3)^2. - _Colin Barker_, Feb 11 2019
%e A279736 Some solutions for n=4:
%e A279736 ..0..1..0. .0..1..0. .0..1..0. .0..1..0. .0..1..1. .0..1..0. .0..1..0
%e A279736 ..1..0..0. .0..1..1. .0..1..1. .0..0..1. .0..0..1. .1..0..1. .0..0..1
%e A279736 ..1..1..1. .1..0..0. .0..1..1. .0..1..0. .1..1..1. .1..1..1. .1..0..1
%e A279736 ..0..1..0. .1..0..1. .0..0..1. .1..0..1. .1..0..1. .0..0..1. .1..1..0
%Y A279736 Column 3 of A279741.
%K A279736 nonn
%O A279736 1,1
%A A279736 _R. H. Hardin_, Dec 18 2016