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A279735 Number of n X 2 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 A279735 #8 Feb 11 2019 14:22:10
%S A279735 0,2,8,26,80,240,708,2062,5944,16990,48220,136032,381768,1066586,
%T A279735 2968040,8230370,22751528,62716752,172447884,473081830,1295113240,
%U A279735 3538749862,9652296628,26285128896,71472896400,194075990450,526312559048
%N A279735 Number of n X 2 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 A279735 R. H. Hardin, <a href="/A279735/b279735.txt">Table of n, a(n) for n = 1..210</a>
%F A279735 Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).
%F A279735 Conjectures from _Colin Barker_, Feb 11 2019: (Start)
%F A279735 G.f.: 2*x^2*(1 - 2*x) / (1 - 3*x + x^2)^2.
%F A279735 a(n) = (-1)*(2^(1-n)*(sqrt(5)*((3-sqrt(5))^n-(3+sqrt(5))^n) + 5*(3-sqrt(5))^n*(2+sqrt(5))*n - 5*(-2+sqrt(5))*(3+sqrt(5))^n*n)) / 25.
%F A279735 (End)
%e A279735 Some solutions for n=4:
%e A279735 ..0..1. .0..0. .0..1. .0..1. .0..1. .0..0. .0..1. .0..0. .0..1. .0..1
%e A279735 ..0..1. .1..1. .0..0. .0..1. .0..0. .1..0. .1..0. .1..0. .0..0. .0..1
%e A279735 ..1..0. .0..1. .1..1. .1..1. .0..1. .1..1. .1..1. .1..0. .1..0. .0..0
%e A279735 ..1..1. .0..1. .1..0. .0..1. .1..0. .0..1. .1..0. .1..0. .1..1. .1..1
%Y A279735 Column 2 of A279741.
%K A279735 nonn
%O A279735 1,2
%A A279735 _R. H. Hardin_, Dec 18 2016