A220547 Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

2, 8, 29, 108, 401, 1490, 5536, 20569, 76424, 283953, 1055026, 3919944, 14564533, 54114452, 201061985, 747044834, 2775641472, 10312882481, 38317465040, 142368356257, 528968939938, 1965381541064, 7302365621709, 27131904192124

Offset: 1

Author

R. H. Hardin, Dec 15 2012

Keywords

• nonn

Comments

Column 2 of A220553.

Examples

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10):
..8..8....0..7....6..4....6..4....8..0....0..0....0..0....0..0....0..8....6..4
..2..2....3..8....0..0....6..4....2..8....8..8....0..8....0..0....8..2....8..8
..6..4....0..2....0..0....0..0....0..2....2..2....0..2....0..0....2..0....2..2
		

Links

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

Crossrefs

Cf. A220553, A000078.

Formula

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

Empirical g.f.: x*(1 + x)*(2 - x^2) / (1 - 3*x - 3*x^2 + x^3 + x^4). - Colin Barker, Mar 13 2018

Empirical: a(n) = A000078(2*n + 3). - Greg Dresden, Jan 10 2021