A268898 Number of n X 2 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

3, 36, 240, 1344, 6912, 33792, 159744, 737280, 3342336, 14942208, 66060288, 289406976, 1258291200, 5435817984, 23353884672, 99857989632, 425201762304, 1803886264320, 7627861917696, 32160715112448, 135239930216448

Offset: 1

Author

R. H. Hardin, Feb 15 2016

Keywords

• nonn

Examples

			Some solutions for n=4:
..2..2. .0..1. .1..0. .0..1. .2..1. .2..0. .1..0. .1..0. .0..1. .0..1
..2..1. .1..0. .1..1. .0..0. .0..1. .0..0. .1..2. .0..1. .0..1. .2..2
..0..2. .1..0. .2..1. .1..1. .0..1. .1..2. .2..0. .0..2. .2..2. .0..0
..2..1. .0..1. .2..1. .2..2. .2..0. .1..0. .0..0. .1..2. .1..1. .0..0
		

Links

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

Crossrefs

Column 2 of A268904.

Formula

Empirical: a(n) = 8*a(n-1) - 16*a(n-2).

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

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

a(n) = 4^(n-1) * (6*n-3).

(End)