A268775 Number of n X 2 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two no more than once.

4, 11, 26, 65, 148, 343, 766, 1709, 3752, 8195, 17746, 38233, 81916, 174767, 371366, 786437, 1660240, 3495259, 7340026, 15379121, 32156324, 67108871, 139810126, 290805085, 603979768, 1252698803, 2594876066, 5368709129, 11095332172

Offset: 1

Author

R. H. Hardin, Feb 13 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 2 of A268781.

Formula

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

Conjectures from Colin Barker, Jan 15 2019: (Start)

G.f.: x*(4 + 3*x - 8*x^2 - 4*x^3) / ((1 + x)^2*(1 - 2*x)^2).

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

(End)