A220683 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

1, 12, 94, 745, 5851, 46027, 362057, 2847943, 22401961, 176214299, 1386105209, 10903131303, 85764249269, 674623302927, 5306600415489, 41741825175435, 328342033045001, 2582745009614887, 20315923985816277, 159805465061769263

Offset: 1

Author

R. H. Hardin, Dec 17 2012

Keywords

• nonn

Comments

Column 3 of A220688.

Examples

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10):
.68.46.47...68.47.00...00.67.48...00.00.00...68.47.00...00.67.48...00.78.00
.28.36.48...23.67.47...36.47.27...68.46.47...23.67.48...38.68.24...38.26.48
.26.46.24...36.34.00...36.34.00...26.34.00...36.46.24...26.24.00...26.46.24
		

Links

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

Crossrefs

Cf. A220688.

Formula

Empirical: a(n) = 6*a(n-1) + 12*a(n-2) + 19*a(n-3) + 16*a(n-4) + 2*a(n-5) for n>6.

Empirical g.f.: x*(1 + 6*x + 10*x^2 + 18*x^3 + 9*x^4 + x^5) / ((1 + x)*(1 - 7*x - 5*x^2 - 14*x^3 - 2*x^4)). - Colin Barker, Aug 02 2018