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

1,2

Comments

Column 3 of A220688.

Links

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

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

Example

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

Crossrefs

Cf. A220688.

Sequence in context: A057410 A045894 A045829 * A009647 A038836 A026860

Adjacent sequences: A220680 A220681 A220682 * A220684 A220685 A220686

Keyword

nonn

Author

R. H. Hardin, Dec 17 2012

Status

approved