A297577 Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 4 neighboring 1s.

3, 11, 36, 102, 370, 1243, 3854, 13078, 43861, 141109, 468638, 1561065, 5101698, 16842125, 55830567, 183595621, 605376713, 2001499842, 6596762626, 21752445702, 71828204711, 236917416288, 781388833534, 2578812375049, 8507768092491

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) + 19*a(n-3) + 4*a(n-4) - 17*a(n-5) - 8*a(n-6).

Empirical g.f.: x*(3 + 8*x + 19*x^2 - 13*x^3 - 25*x^4 - 8*x^5) / ((1 - x)*(1 - 2*x^2 - 21*x^3 - 25*x^4 - 8*x^5)). - Colin Barker, Mar 01 2019

Example

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

Crossrefs

Column 3 of A297582.

Sequence in context: A119092 A119177 A213679 * A119126 A119088 A296391

Adjacent sequences: A297574 A297575 A297576 * A297578 A297579 A297580

Keyword

nonn

Author

R. H. Hardin, Jan 01 2018

Status

approved