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A220705
Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.
1
1, 5, 12, 37, 107, 317, 932, 2749, 8101, 23881, 70392, 207497, 611639, 1802937, 5314536, 15665721, 46178025, 136119501, 401241028, 1182742829, 3486384739, 10276856693, 30293209548, 89295644789, 263217806797, 775890178961
OFFSET
1,2
COMMENTS
Column 5 of A220708.
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - a(n-4) - 2*a(n-5) - a(n-6).
Empirical g.f.: x*(1 + 3*x - x^2 - 2*x^3 - 2*x^4 - x^5) / ((1 - x)*(1 + x)*(1 - 2*x - 2*x^2 - 2*x^3 - x^4)). - Colin Barker, Aug 02 2018
EXAMPLE
Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
.00.00.67.47.00...00.00.00.00.00...00.00.00.00.00...00.67.47.00.00
.00.36.34.67.47...00.67.47.67.47...00.00.00.00.00...36.34.00.00.00
.00.00.36.34.00...36.34.36.34.00...00.00.00.00.00...00.00.00.00.00
CROSSREFS
Cf. A220708.
Sequence in context: A300534 A359189 A297909 * A034752 A095310 A122299
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 18 2012
STATUS
approved