A220713 - OEIS

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

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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):