A296322 Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1s.

1, 5, 11, 23, 54, 122, 278, 634, 1438, 3274, 7451, 16943, 38547, 87691, 199477, 453789, 1032300, 2348324, 5342108, 12152500, 27645148, 62888676, 143062485, 325446157, 740342261, 1684169937, 3831239423, 8715507347, 19826499874, 45102377086

Offset: 1

Author

R. H. Hardin, Dec 10 2017

Keywords

• nonn

Examples

			Some solutions for n=5:
..1..1..0. .0..0..1. .0..0..0. .0..0..0. .1..1..0. .0..0..0. .0..1..0
..1..0..0. .0..1..1. .0..0..0. .0..0..0. .1..0..0. .0..1..1. .1..1..0
..0..0..0. .0..0..0. .0..0..0. .1..1..0. .0..1..1. .0..1..0. .0..0..0
..0..1..0. .0..1..0. .0..0..1. .1..0..0. .1..0..1. .0..0..0. .0..1..0
..1..1..0. .1..1..0. .0..1..1. .0..0..0. .1..1..0. .0..0..0. .1..1..0
		

Links

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

Crossrefs

Column 3 of A296327.

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3) - 2*a(n-4) + 4*a(n-5) - 3*a(n-6) + 2*a(n-7) - a(n-8).

Empirical g.f.: x*(1 + 3*x + 2*x^2 + 2*x^3 + x^4 - x^5 + x^6 - x^7) / ((1 + x^2)*(1 - 2*x - 2*x^3 + 2*x^4 - 2*x^5 + x^6)). - Colin Barker, Feb 23 2019