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

0,2

Links

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

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

Example

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

Crossrefs

Column 3 of A297595.

Sequence in context: A211294 A211297 A370227 * A244934 A291594 A007046

Adjacent sequences: A297587 A297588 A297589 * A297591 A297592 A297593

Keyword

nonn

Author

R. H. Hardin, Jan 01 2018

Extensions

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

Status

approved