A232032 Number of (n+1) X (2+1) 0..1 arrays with every element equal to some horizontal, vertical or antidiagonal neighbor, with top left element zero.

11, 76, 521, 3588, 24719, 170270, 1172854, 8078859, 55648831, 383320506, 2640389883, 18187544432, 125279518221, 862950891715, 5944181874953, 40944737993493, 282035712335780, 1942719551542674, 13381848790314938

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(11 - x - 11*x^2 - 4*x^3 + 5*x^4 + 5*x^5 - x^7) / (1 - 7*x + 5*x^3 + 2*x^4 + x^5 - 2*x^6 - 2*x^7). - Colin Barker, Oct 02 2018

Example

Some solutions for n=6:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1
..1..0..0....1..1..0....0..0..1....0..0..0....0..1..1....0..1..1....0..1..0
..1..1..0....1..1..0....1..1..0....0..1..0....1..0..0....0..0..1....0..0..0
..1..1..1....1..0..1....0..0..1....1..1..1....1..1..0....0..0..0....1..0..1
..1..0..1....1..0..1....0..0..1....0..1..0....1..1..1....0..1..0....1..1..0
..1..0..1....0..0..0....1..1..1....0..0..0....0..0..1....1..1..0....0..0..0
..1..0..1....1..1..1....0..0..1....1..1..1....1..1..1....1..1..0....1..1..0

Crossrefs

Column 2 of A232038.

Sequence in context: A256597 A245561 A056914 * A272395 A305727 A218395

Adjacent sequences: A232029 A232030 A232031 * A232033 A232034 A232035

Keyword

nonn

Author

R. H. Hardin, Nov 17 2013

Status

approved