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A220709
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Number of ways to reciprocally link elements of a 4 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, 5, 13, 37, 105, 298, 846, 2404, 6826, 19394, 55081, 156473, 444445, 1262497, 3586113, 10186570, 28935186, 82191652, 233468038, 663174914, 1883771569, 5350922525, 15199487245, 43174696525, 122639283705, 348361331050
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OFFSET
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1,3
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COMMENTS
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Row 4 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) = a(n-1) + 6*a(n-2) - 6*a(n-4) - a(n-5) + a(n-6) for n>7.
Empirical g.f.: x*(1 - 2*x^2 + 2*x^3 - 3*x^5 + x^6) / ((1 - x)*(1 + x)*(1 - x - 5*x^2 - x^3 + x^4)). - Colin Barker, Aug 02 2018
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EXAMPLE
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All 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
.00.67.47...00.00.00...36.34.00...36.34.00...00.00.00
.36.34.00...00.00.00...00.00.00...00.67.47...00.67.47
.00.00.00...00.00.00...00.00.00...36.34.00...36.34.00
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CROSSREFS
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Cf. A220708.
Sequence in context: A269803 A298417 A193642 * A182312 A071100 A199108
Adjacent sequences: A220706 A220707 A220708 * A220710 A220711 A220712
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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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