A297590 Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 5 neighboring 1s.

1, 3, 9, 25, 69, 205, 597, 1701, 4949, 14389, 41493, 120149, 348437, 1008021, 2917653, 8451605, 24467733, 70830869, 205101333, 593841429, 1719269653, 4977934613, 14412904725, 41729378581, 120820070677, 349814724885, 1012822636821, 2932443592981, 8490378131733

Offset: 0

Author

R. H. Hardin, Jan 01 2018

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000 (terms n = 1..210 from R. H. Hardin)

Crossrefs

Column 3 of A297595.

Formula

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

Empirical g.f.: 1 + x*(3 + 6*x + 10*x^2 - 4*x^3 - 16*x^4 - 8*x^5) / ((1 - x)*(1 - 2*x^2 - 12*x^3 - 16*x^4 - 8*x^5)). - Colin Barker, Mar 01 2019

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 01 2019