A296582 Number of n X 2 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 2 or 3 neighboring 1s.

3, 9, 22, 62, 172, 480, 1358, 3849, 10951, 31232, 89193, 254996, 729509, 2087983, 5978057, 17119192, 49030629, 140440575, 402295454, 1152434018, 3301409215, 9457817513, 27094931531, 77622729861, 222378228416, 637084878266

Offset

1,1

Links

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

Formula

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

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

Example

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

Crossrefs

Column 2 of A296588.

Sequence in context: A114697 A032284 A329163 * A203454 A197666 A146009

Adjacent sequences: A296579 A296580 A296581 * A296583 A296584 A296585

Keyword

nonn

Author

R. H. Hardin, Dec 16 2017

Status

approved