A220647 Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly two king-move neighbors, without 3-loops.

1, 4, 23, 83, 344, 1441, 5881, 24220, 99767, 410363, 1688864, 6950497, 28602385, 117707380, 484400087, 1993438499, 8203560488, 33759953377, 138931649065, 571742660236, 2352881191991, 9682765028939, 39847290050288, 163982758812193

Offset

1,2

Comments

Column 2 of A220652.

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) + 8*a(n-3) - 6*a(n-4).

Empirical g.f.: x*(1 + x + 8*x^2 - 6*x^3) / (1 - 3*x - 3*x^2 - 8*x^3 + 6*x^4). - Colin Barker, Aug 02 2018

Example

Some solutions for n=3 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10):
.68.48...68.48...00.78...69.47...00.00...89.00...00.00...69.47...89.00...00.00
.26.24...29.27...39.27...39.18...00.00...28.17...89.78...38.17...29.17...69.47
.00.00...36.14...36.14...00.12...00.00...23.00...23.12...23.00...36.14...36.14

Crossrefs

Cf. A220652.

Sequence in context: A305771 A219465 A317120 * A014585 A305588 A317006

Adjacent sequences: A220644 A220645 A220646 * A220648 A220649 A220650

Keyword

nonn

Author

R. H. Hardin, Dec 17 2012

Status

approved