A220633 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.

1, 1, 3, 12, 44, 158, 564, 2010, 7160, 25502, 90828, 323490, 1152128, 4103366, 14614356, 52049802, 185378120, 660233966, 2351458140, 8374842354, 29827443344, 106232014742, 378350930916, 1347516822234, 4799252328536, 17092790630078

Offset

1,3

Comments

Row 3 of A220632.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - a(n-2) - 2*a(n-3) for n>5.

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

Example

All solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
.00.00.00...00.67.47...00.00.00
.00.67.47...36.34.00...00.00.00
.36.34.00...00.00.00...00.00.00

Crossrefs

Cf. A220632.

Sequence in context: A356888 A167477 A190051 * A296225 A109437 A331473

Adjacent sequences: A220630 A220631 A220632 * A220634 A220635 A220636

Keyword

nonn

Author

R. H. Hardin, Dec 17 2012

Status

approved