A296124 Number of n X 4 0..1 arrays with each 1 adjacent to 2 or 5 king-move neighboring 1s.

1, 13, 30, 74, 287, 841, 2463, 7953, 24428, 74660, 233017, 721069, 2226921, 6907921, 21399342, 66252970, 205308499, 636102161, 1970540971, 6105562057, 18917255184, 58610713832, 181598709121, 562663895105, 1743342282089, 5401567886229

Offset: 1

Author

R. H. Hardin, Dec 05 2017

Keywords

• nonn

Examples

			Some solutions for n=7:
..0..1..0..0. .0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..1..0
..1..0..1..0. .0..0..1..0. .0..0..0..0. .0..0..1..0. .1..1..1..0
..1..0..0..1. .0..0..0..0. .0..0..1..0. .0..0..0..0. .0..1..1..1
..1..0..1..0. .0..0..0..1. .0..1..1..0. .0..1..1..0. .0..1..0..0
..1..0..0..1. .0..0..1..1. .0..0..0..0. .1..0..0..1. .0..0..0..1
..0..1..1..0. .1..0..0..0. .1..0..0..0. .1..0..0..1. .0..0..1..1
..0..0..0..0. .1..1..0..0. .1..1..0..0. .0..1..1..0. .0..0..0..0
		

Links

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

Crossrefs

Column 4 of A296128.

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) + 5*a(n-3) - 18*a(n-4) - 14*a(n-5) + 3*a(n-6) + a(n-7) + a(n-8) - a(n-9).

Empirical g.f.: x*(1 + x)*(1 + 9*x - 19*x^2 - 15*x^3 + 3*x^4 + x^5 + x^6 - x^7) / (1 - 3*x - x^2 - 5*x^3 + 18*x^4 + 14*x^5 - 3*x^6 - x^7 - x^8 + x^9). - Colin Barker, Feb 22 2019