A220713 Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly two king-move neighbors, without consecutive collinear links.

1, 8, 26, 118, 463, 1930, 7843, 32209, 131698, 539466, 2208130, 9041065, 37013388, 151537869, 620403077, 2539982216, 10398860814, 42573713750, 174299854287, 713596365222, 2921515440791, 11960897338493, 48968785309970

Offset

1,2

Comments

Column 2 of A220718.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 8*a(n-2) + 3*a(n-3) - 2*a(n-4) - 3*a(n-5) + a(n-6).

Empirical g.f.: x*(1 + 6*x + 2*x^2 - x^3 - 3*x^4 + x^5) / (1 - 2*x - 8*x^2 - 3*x^3 + 2*x^4 + 3*x^5 - x^6). - Colin Barker, Aug 02 2018

Example

Some solutions for n=3 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10):
.69.47...68.47...89.00...00.00...00.00...00.00...00.78...69.48...00.00...89.78
.36.14...23.00...29.17...69.47...68.48...00.78...39.27...00.12...68.47...23.12
.00.00...00.00...36.14...36.14...26.24...36.24...36.14...00.00...23.00...00.00

Crossrefs

Cf. A220718.

Sequence in context: A140788 A082573 A112645 * A260962 A274733 A223312

Adjacent sequences: A220710 A220711 A220712 * A220714 A220715 A220716

Keyword

nonn

Author

R. H. Hardin, Dec 18 2012

Status

approved