A268768 Number of n X 2 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

3, 12, 32, 100, 248, 620, 1456, 3380, 7656, 17148, 37920, 83140, 180824, 390796, 839824, 1796180, 3825352, 8116764, 17165568, 36195300, 76118840, 159694252, 334301552, 698429300, 1456510888, 3032326460, 6303262176, 13083742980

Offset: 1

Author

R. H. Hardin, Feb 13 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 2 of A268774.

Formula

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

Conjectures from Colin Barker, Jan 14 2019: (Start)

G.f.: x*(3 + 6*x - x^2 + 12*x^3 + 12*x^4) / ((1 + x)^2*(1 - 2*x)^2).

a(n) = (4/27)*(7*((-1)^n-2^n) + 3*((-1)^n + 2^(2+n))*n) for n>1.

(End)