A296329 Number of n X 2 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0 or 2 neighboring 1s.

3, 8, 19, 47, 116, 286, 705, 1738, 4285, 10564, 26044, 64208, 158296, 390257, 962125, 2371987, 5847808, 14416967, 35543051, 87626508, 216031114, 532595025, 1313039846, 3237119305, 7980672808, 19675252120, 48506630368, 119586431488

Offset

1,1

Comments

Column 2 of A296335.

Links

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

Formula

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

Empirical g.f.: x*(3 + 5*x + 5*x^2 + 3*x^3 + x^4) / (1 - x - 2*x^2 - 3*x^3 - 2*x^4 - x^5). - Colin Barker, Mar 22 2018

Example

Some solutions for n=5:
..1..0. .0..0. .1..0. .0..0. .1..0. .0..0. .1..0. .1..0. .0..0. .1..0
..0..0. .1..0. .0..0. .0..0. .0..1. .0..0. .0..0. .0..1. .0..1. .0..1
..0..0. .0..0. .0..0. .0..1. .0..0. .1..1. .1..0. .0..0. .0..0. .0..0
..0..1. .0..0. .0..0. .0..0. .0..1. .1..0. .0..0. .0..0. .0..0. .0..1
..1..1. .1..0. .0..1. .0..1. .0..0. .0..1. .0..0. .1..0. .1..0. .1..1

Crossrefs

Cf. A296335.

Sequence in context: A121811 A370033 A244208 * A339525 A295045 A181849

Adjacent sequences: A296326 A296327 A296328 * A296330 A296331 A296332

Keyword

nonn

Author

R. H. Hardin, Dec 10 2017

Status

approved