A220733 - OEIS

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A220733

Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, diagonal and antidiagonal neighbors, without consecutive collinear links.

1, 5, 22, 72, 258, 949, 3403, 12241, 44192, 159272, 573952, 2069009, 7457849, 26881189, 96893542, 349253376, 1258880466, 4537629845, 16355874451, 58954682593, 212501925632, 765962408016, 2760908604224, 9951684619105

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OFFSET

1,2

COMMENTS

Column 3 of A220738.

LINKS

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

FORMULA

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) + 9*a(n-3) + 4*a(n-4) - a(n-5).

Empirical g.f.: x*(1 + 3*x + 9*x^2 + 4*x^3 - x^4) / (1 - 2*x - 3*x^2 - 9*x^3 - 4*x^4 + x^5). - Colin Barker, Aug 03 2018

EXAMPLE

Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10):