cp's OEIS Frontend

A279262 Number of n X 2 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.

%I A279262 #9 Feb 26 2018 09:15:06
%S A279262 0,4,10,20,38,68,120,208,358,612,1042,1768,2992,5052,8514,14324,24062,
%T A279262 40364,67624,113160,189150,315844,526890,878160,1462368,2433268,
%U A279262 4045690,6721748,11160278,18517652,30706392,50888128,84287062,139531812
%N A279262 Number of n X 2 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.
%C A279262 Column 2 of A279268.
%H A279262 R. H. Hardin, <a href="/A279262/b279262.txt">Table of n, a(n) for n = 1..210</a>
%F A279262 Empirical: a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) + a(n-5).
%F A279262 Conjectures from _Colin Barker_, Feb 26 2018: (Start)
%F A279262 G.f.: 2*x^2*(1 + x)*(2 - 3*x) / ((1 - x)*(1 - x - x^2)^2).
%F A279262 a(n) = (1/25)*(2^(-n)*(-25*2^(2+n)+(50-6*sqrt(5))*(1-sqrt(5))^n + 50*(1+sqrt(5))^n + 6*sqrt(5)*(1+sqrt(5))^n - 5*(1-sqrt(5))^n*(1+sqrt(5))*n + 5*(-1+sqrt(5))*(1+sqrt(5))^n*n)).
%F A279262 (End)
%e A279262 Some solutions for n=4:
%e A279262 ..0..0. .0..0. .0..0. .0..1. .0..1. .0..1. .0..0. .0..0. .0..1. .0..1
%e A279262 ..1..1. .1..1. .1..0. .1..0. .0..1. .1..0. .0..1. .0..1. .0..0. .0..0
%e A279262 ..0..0. .1..0. .0..1. .0..1. .1..0. .0..0. .1..0. .1..0. .0..1. .1..1
%e A279262 ..1..0. .0..1. .1..0. .0..0. .0..0. .1..1. .1..0. .0..1. .1..0. .0..0
%Y A279262 Cf. A279268.
%K A279262 nonn
%O A279262 1,2
%A A279262 _R. H. Hardin_, Dec 08 2016