A295115 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

3, 9, 26, 77, 226, 665, 1960, 5769, 16983, 49998, 147198, 433361, 1275825, 3756068, 11058011, 32555211, 95843749, 282167522, 830711657, 2445646047, 7200072866, 21197281911, 62405585330, 183724361820, 540891347189, 1592404221036

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(3 + 6*x + 8*x^2 + 9*x^3 + 5*x^4 - 6*x^5 - 10*x^6 - 4*x^7 + x^8 + x^9) / (1 - x - 3*x^2 - 5*x^3 - 7*x^4 - 7*x^5 + x^6 + 8*x^7 + 5*x^8 - x^10). - Colin Barker, Feb 22 2019

Example

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

Crossrefs

Column 3 of A295120.

Sequence in context: A101169 A119826 A027915 * A114982 A133405 A368088

Adjacent sequences: A295112 A295113 A295114 * A295116 A295117 A295118

Keyword

nonn

Author

R. H. Hardin, Nov 15 2017

Status

approved