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

Author

R. H. Hardin, Dec 17 2012

Keywords

• nonn

Comments

Column 3 of A220621.

Examples

			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
		

Links

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

Crossrefs

Cf. A220621.

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