A296315 Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

3, 11, 32, 96, 295, 902, 2747, 8380, 25577, 78021, 238029, 726211, 2215568, 6759403, 20622067, 62915288, 191946374, 585603549, 1786600798, 5450687951, 16629344149, 50733978916, 154782809780, 472222339285, 1440689299042, 4395356771500

Offset: 1

Author

R. H. Hardin, Dec 10 2017

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A296320.

Formula

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

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