A296536 Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 or 4 neighboring 1s.

1, 5, 16, 37, 96, 254, 654, 1709, 4472, 11621, 30257, 78899, 205534, 535394, 1395017, 3634476, 9468722, 24669483, 64272370, 167449745, 436262198, 1136608103, 2961236309, 7714995835, 20100110050, 52367403411, 136434332477, 355456392933

Offset: 1

Author

R. H. Hardin, Dec 15 2017

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A296541.

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + 5*a(n-3) + a(n-4) + 6*a(n-5) + 7*a(n-6) + a(n-7) + 3*a(n-8) + 3*a(n-9) - 3*a(n-10) - 4*a(n-11) - a(n-12).

Empirical g.f.: x*(1 + 3*x + 7*x^2 + 5*x^3 + 12*x^4 + 8*x^5 + 4*x^6 + 6*x^7 - 7*x^9 - 5*x^10 - x^11) / ((1 + x^2 + x^3)*(1 - 2*x - 4*x^3 + x^4 - 2*x^5 - 4*x^6 + 3*x^8 + x^9)). - Colin Barker, Feb 23 2019