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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
1, 5, 22, 72, 258, 949, 3403, 12241, 44192, 159272, 573952, 2069009, 7457849, 26881189, 96893542, 349253376, 1258880466, 4537629845, 16355874451, 58954682593, 212501925632, 765962408016, 2760908604224, 9951684619105 (list; graph; refs; listen; history; text; internal format)
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):

.00.69.47...00.00.00...00.69.47...69.47.00...00.79.00...00.00.00...69.47.00

.69.34.17...00.69.47...00.39.17...39.16.47...39.00.17...69.49.00...39.17.00

.00.13.00...00.36.14...00.36.14...00.13.00...00.13.00...00.16.14...36.14.00

CROSSREFS

Cf. A220738.

Sequence in context: A000345 A011846 A241694 * A338707 A058750 A058752

Adjacent sequences:  A220730 A220731 A220732 * A220734 A220735 A220736

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 18 2012

STATUS

approved

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Last modified September 28 15:31 EDT 2021. Contains 347716 sequences. (Running on oeis4.)