A268769 Number of n X 3 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

12, 32, 112, 446, 1524, 5214, 17000, 54822, 173244, 541910, 1676448, 5146030, 15683076, 47518926, 143238872, 429867830, 1285009740, 3828046534, 11368576272, 33669165246, 99465517716, 293175780030, 862355454792, 2531766659654

Offset: 1

Author

R. H. Hardin, Feb 13 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A268774.

Formula

Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - 16*a(n-3) - a(n-4) + 12*a(n-5) - 4*a(n-6) for n>8.

Empirical g.f.: 2*x*(6 - 8*x - 20*x^2 + 63*x^3 + 20*x^4 - 47*x^5 + 4*x^6 + 4*x^7) / (1 - 2*x - 3*x^2 + 2*x^3)^2. - Colin Barker, Jan 15 2019