login
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
OFFSET
1,2
COMMENTS
Column 3 of A220738.
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 18 2012
STATUS
approved