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A220563
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Number of ways to reciprocally link elements of an 2 X n array either to themselves or to exactly one horizontal or antidiagonal neighbor.
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1
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1, 5, 14, 47, 149, 481, 1544, 4965, 15957, 51293, 164870, 529947, 1703417, 5475329, 17599456, 56570281, 181834969, 584475733, 1878691886, 6038716423, 19410365421, 62391120801, 200545011400, 644615789581, 2072001259341, 6660074556205
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OFFSET
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1,2
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COMMENTS
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For n > 0, a(n) is the number of ways to tile the S-shaped figure of length n below with squares and dominoes. For instance, a(4) is the number of ways to tile this figure with squares and dominoes.
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(End)
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LINKS
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FORMULA
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a(n) = 2*a(n-1) + 4*a(n-2) - a(n-4).
G.f.: x*(1 + 3*x - x^3) / ((1 + x)*(1 - 3*x - x^2 + x^3). - Colin Barker, Jul 31 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):
0 6 4 0 0 0 0 7 0 6 4 0 0 0 0 0 7 0 0 6 4
0 6 4 0 0 0 3 6 4 0 0 0 0 6 4 3 0 0 0 0 0
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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