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

Author

R. H. Hardin, Dec 17 2012

Keywords

• nonn

Comments

Row 3 of A220632.

Examples

			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
		

Links

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

Crossrefs

Cf. A220632.

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