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A220705
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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.
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1
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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
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OFFSET
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1,2
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COMMENTS
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Column 5 of A220708.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
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FORMULA
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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
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EXAMPLE
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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
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CROSSREFS
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Cf. A220708.
Sequence in context: A300534 A359189 A297909 * A034752 A095310 A122299
Adjacent sequences: A220702 A220703 A220704 * A220706 A220707 A220708
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Dec 18 2012
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STATUS
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approved
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