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.

0, 2, 8, 26, 80, 240, 708, 2062, 5944, 16990, 48220, 136032, 381768, 1066586, 2968040, 8230370, 22751528, 62716752, 172447884, 473081830, 1295113240, 3538749862, 9652296628, 26285128896, 71472896400, 194075990450, 526312559048

Offset: 1

Author

R. H. Hardin, Dec 18 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 2 of A279741.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).

Conjectures from Colin Barker, Feb 11 2019: (Start)

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

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.

(End)