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.

0, 4, 10, 20, 38, 68, 120, 208, 358, 612, 1042, 1768, 2992, 5052, 8514, 14324, 24062, 40364, 67624, 113160, 189150, 315844, 526890, 878160, 1462368, 2433268, 4045690, 6721748, 11160278, 18517652, 30706392, 50888128, 84287062, 139531812

Offset: 1

Author

R. H. Hardin, Dec 08 2016

Keywords

• nonn

Comments

Column 2 of A279268.

Examples

			Some solutions for n=4:
..0..0. .0..0. .0..0. .0..1. .0..1. .0..1. .0..0. .0..0. .0..1. .0..1
..1..1. .1..1. .1..0. .1..0. .0..1. .1..0. .0..1. .0..1. .0..0. .0..0
..0..0. .1..0. .0..1. .0..1. .1..0. .0..0. .1..0. .1..0. .0..1. .1..1
..1..0. .0..1. .1..0. .0..0. .0..0. .1..1. .1..0. .0..1. .1..0. .0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A279268.

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) + a(n-5).

Conjectures from Colin Barker, Feb 26 2018: (Start)

G.f.: 2*x^2*(1 + x)*(2 - 3*x) / ((1 - x)*(1 - x - x^2)^2).

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)).

(End)