A281199 Number of n X 2 0..1 arrays with no element equal to more than one 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, 10, 38, 130, 420, 1308, 3970, 11822, 34690, 100610, 289032, 823800, 2332418, 6566290, 18394910, 51310978, 142587180, 394905492, 1090444930, 3002921270, 8249479162, 22612505090, 61857842448, 168903452400, 460409998850

Offset: 1

Author

R. H. Hardin, Jan 17 2017

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 2 of A281205.

Formula

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

Conjectures from Colin Barker, Feb 16 2019: (Start)

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

a(n) = (2^(-n)*(2*sqrt(5)*((3-sqrt(5))^n - (3+sqrt(5))^n) - 5*(3-sqrt(5))^n*(1+sqrt(5))*n + 5*(-1+sqrt(5))*(3+sqrt(5))^n*n)) / 25.

(End)