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

1,1

Comments

Column 2 of A220553.

Links

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

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

Example

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

Crossrefs

Cf. A220553, A000078.

Sequence in context: A369268 A369299 A011367 * A261774 A345131 A150733

Adjacent sequences: A220544 A220545 A220546 * A220548 A220549 A220550

Keyword

nonn

Author

R. H. Hardin, Dec 15 2012

Status

approved