A268900 Number of n X 4 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

36, 696, 9720, 118584, 1347192, 14644152, 154472184, 1594323000, 16185567096, 162200044728, 1608569870328, 15816054042936, 154394813276280, 1498006261495224, 14458132831535352, 138907883786523192

Offset: 1

Author

R. H. Hardin, Feb 15 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 4 of A268904.

Formula

Empirical: a(n) = 18*a(n-1) - 81*a(n-2) for n>3.

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

G.f.: 12*x*(3 + 4*x + 9*x^2) / (1 - 9*x)^2.

a(n) = 8 * 3^(2*n-3) * (16*n-3) for n>1.

(End)