A220629 Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal or antidiagonal neighbors.

1, 8, 44, 257, 1481, 8560, 49448, 285669, 1650333, 9534128, 55079528, 318199485, 1838267585, 10619840324, 61351790884, 354434918989, 2047603011865, 11829190267612, 68338316351600, 394796716945057, 2280776817922653

Offset

1,2

Comments

Column 5 of A220632.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 9*a(n-2) + 7*a(n-3) + 2*a(n-4) - a(n-5).

Empirical g.f.: x*(1 + 3*x - x^2)*(1 + x + x^2) / ((1 + x)*(1 - 5*x - 4*x^2 - 3*x^3 + x^4)). - Colin Barker, Aug 01 2018

Example

Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
.00.67.46.46.47...00.67.46.47.00...00.00.00.00.00...00.00.67.46.47
.36.47.00.36.47...36.46.34.67.47...00.67.46.47.00...00.37.67.34.00
.36.46.46.34.00...00.00.36.34.00...36.46.34.00.00...36.34.00.00.00

Crossrefs

Cf. A220632.

Sequence in context: A147828 A155604 A126476 * A210118 A112908 A264819

Adjacent sequences: A220626 A220627 A220628 * A220630 A220631 A220632

Keyword

nonn

Author

R. H. Hardin, Dec 17 2012

Status

approved