A220616 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.

3, 21, 125, 765, 4657, 28373, 172833, 1052829, 6413369, 39067429, 237981569, 1449678893, 8830805161, 53793374581, 327685538769, 1996115937021, 12159458878905, 74070066514885, 451202212873441, 2748525099013581

Offset

1,1

Comments

Column 3 of A220621.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 4*a(n-2) - 10*a(n-3) + 4*a(n-4).

Empirical g.f.: x*(1 + 2*x)*(3 - 6*x + 2*x^2) / (1 - 7*x + 4*x^2 + 10*x^3 - 4*x^4). - Colin Barker, Aug 01 2018

Example

Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10):
..0..6..4....0..7..0....0..7..0....0..0..0....6..4..0....0..6..4....0..9..7
..0..6..4....3..6..4....3..7..7....0..9..7....0..7..0....6..4..0....0..3..1
..0..0..0....0..6..4....3..3..0....0..3..1....3..0..0....6..4..0....6..4..0

Crossrefs

Cf. A220621.

Sequence in context: A004658 A034552 A356889 * A273803 A036754 A121447

Adjacent sequences: A220613 A220614 A220615 * A220617 A220618 A220619

Keyword

nonn

Author

R. H. Hardin, Dec 17 2012

Status

approved