A220558 Number of ways to reciprocally link elements of an n X 4 array either to themselves or to exactly one horizontal or antidiagonal neighbor.

5, 47, 430, 3966, 36640, 338581, 3128843, 28913910, 267196106, 2469184016, 22817958901, 210862878471, 1948603453870, 18007225586854, 166406444930000, 1537777420552101, 14210744037917219, 131322806156626838

Offset

1,1

Comments

Column 4 of A220562.

Links

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

Formula

Empirical: a(n) = 11*a(n-1) - 17*a(n-2) + 7*a(n-3) - a(n-4).

Empirical g.f.: x*(5 - 8*x - 2*x^2) / (1 - 11*x + 17*x^2 - 7*x^3 + x^4). - Colin Barker, Jul 31 2018

Example

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

Crossrefs

Cf. A220562.

Sequence in context: A198854 A200814 A181582 * A241372 A124267 A124450

Adjacent sequences: A220555 A220556 A220557 * A220559 A220560 A220561

Keyword

nonn

Author

R. H. Hardin, Dec 16 2012

Status

approved