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A220710
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Number of ways to reciprocally link elements of an 5 X n 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, 1, 8, 28, 107, 405, 1520, 5706, 21418, 80390, 301736, 1132543, 4250895, 15955408, 59887275, 224782132, 843701335, 3166765105, 11886195940, 44613876758, 167454575870, 628527215306, 2359126067724, 8854788952291, 33235734276043
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OFFSET
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1,3
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COMMENTS
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Row 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) = 3*a(n-1) + 7*a(n-2) - 14*a(n-3) - 11*a(n-4) + 17*a(n-5) + 5*a(n-6) - 6*a(n-7) for n>11.
Empirical g.f.: x*(1 - 2*x - 2*x^2 + 11*x^3 - 8*x^4 - 6*x^5 + 14*x^6 - 18*x^7 - 3*x^8 + 18*x^9 - 8*x^10) / ((1 - x)*(1 + x)*(1 - 3*x - 6*x^2 + 11*x^3 + 5*x^4 - 6*x^5)). - 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):
.00.00.00...00.00.00...00.67.47...00.67.47...00.00.00...00.00.00...00.00.00
.00.67.47...00.00.00...36.34.00...36.34.00...00.00.00...00.67.47...00.00.00
.36.34.00...00.00.00...00.00.00...00.00.00...00.67.47...36.34.00...00.00.00
.00.00.00...00.67.47...00.00.00...00.67.47...36.34.00...00.67.47...00.00.00
.00.00.00...36.34.00...00.00.00...36.34.00...00.00.00...36.34.00...00.00.00
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CROSSREFS
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Cf. A220708.
Sequence in context: A153365 A317149 A316879 * A260935 A289608 A317607
Adjacent sequences: A220707 A220708 A220709 * A220711 A220712 A220713
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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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