A269012 Number of 2 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

0, 4, 8, 36, 88, 272, 696, 1900, 4856, 12588, 31792, 80288, 200304, 498004, 1229672, 3024948, 7407496, 18079664, 43980072, 106688956, 258132824, 623113020, 1500935776, 3608439104, 8659683552, 20747930788, 49635222728, 118576046148

Offset: 1

Author

R. H. Hardin, Feb 17 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 2 of A269011.

Formula

Empirical: a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3) - 9*a(n-4).

Conjectures from Colin Barker, Jan 18 2019: (Start)

G.f.: 4*x^2 / (1 - x - 3*x^2)^2.

a(n) = 4*(-((1/2)*(1+sqrt(13)))^n*(sqrt(13)-13*n) + ((1/2)*(1-sqrt(13)))^n*(sqrt(13)+13*n)) / 169.

(End)