A232031 Number of (n+1) X (1+1) 0..1 arrays with every element equal to some horizontal, vertical or antidiagonal neighbor, with top left element zero.

3, 11, 37, 129, 450, 1568, 5464, 19041, 66354, 231230, 805789, 2808009, 9785334, 34099877, 118831060, 414101811, 1443059667, 5028766229, 17524216333, 61068290730, 212810436816, 741600615908, 2584325664397, 9005843571858

Offset

1,1

Comments

Column 1 of A232038.

Links

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

Formula

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

Empirical g.f.: x*(3 - x - x^2) / (1 - 4*x + 2*x^2 - x^3 + x^4). - Colin Barker, Mar 19 2018

Example

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

Crossrefs

Cf. A232038.

Sequence in context: A046722 A214996 A180168 * A047102 A109000 A183511

Adjacent sequences: A232028 A232029 A232030 * A232032 A232033 A232034

Keyword

nonn

Author

R. H. Hardin, Nov 17 2013

Status

approved