A220733 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, diagonal and antidiagonal neighbors, without consecutive collinear links.

1, 5, 22, 72, 258, 949, 3403, 12241, 44192, 159272, 573952, 2069009, 7457849, 26881189, 96893542, 349253376, 1258880466, 4537629845, 16355874451, 58954682593, 212501925632, 765962408016, 2760908604224, 9951684619105

Offset

1,2

Comments

Column 3 of A220738.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) + 9*a(n-3) + 4*a(n-4) - a(n-5).

Empirical g.f.: x*(1 + 3*x + 9*x^2 + 4*x^3 - x^4) / (1 - 2*x - 3*x^2 - 9*x^3 - 4*x^4 + x^5). - Colin Barker, Aug 03 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):
.00.69.47...00.00.00...00.69.47...69.47.00...00.79.00...00.00.00...69.47.00
.69.34.17...00.69.47...00.39.17...39.16.47...39.00.17...69.49.00...39.17.00
.00.13.00...00.36.14...00.36.14...00.13.00...00.13.00...00.16.14...36.14.00

Crossrefs

Cf. A220738.

Sequence in context: A000345 A011846 A241694 * A338707 A058750 A058752

Adjacent sequences: A220730 A220731 A220732 * A220734 A220735 A220736

Keyword

nonn

Author

R. H. Hardin, Dec 18 2012

Status

approved