A297221 Number of n X 5 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s.

6, 33, 182, 997, 5570, 30946, 171851, 955316, 5308160, 29497088, 163916530, 910869797, 5061672943, 28127490455, 156303166524, 868569845751, 4826603668246, 26821221189069, 149044329620412, 828232684722634

Offset: 1

Author

R. H. Hardin, Dec 27 2017

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 5 of A297224.

Formula

Empirical: a(n) = a(n-1) + 16*a(n-2) + 45*a(n-3) + 39*a(n-4) - 3*a(n-5) - 21*a(n-6) + 8*a(n-7) - 4*a(n-8) + a(n-9).

Empirical g.f.: x*(6 + 27*x + 53*x^2 + 17*x^3 - 58*x^4 - 35*x^5 + 47*x^6 - 13*x^7 + x^8) / ((1 + 2*x + x^2 - x^3)*(1 - 3*x - 11*x^2 - 19*x^3 + 7*x^4 - 3*x^5 + x^6)). - Colin Barker, Feb 26 2019