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A306447
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Number of (undirected) Hamiltonian cycles in the n-antiprism graph.
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1
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3, 9, 16, 29, 56, 110, 225, 469, 991, 2110, 4511, 9666, 20736, 44511, 95575, 205253, 440828, 946817, 2033628, 4367986, 9381949, 20151433, 43283195, 92967882, 199685571, 428904390, 921243268, 1978737467, 4250128235, 9128846273, 19607840040, 42115660645
(list;
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history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Extended to a(1)-a(2) using the formula/recurrence.
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Antiprism Graph
Eric Weisstein's World of Mathematics, Hamiltonian Cycle
Index entries for linear recurrences with constant coefficients, signature (3,-1,-2,0,1).
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FORMULA
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a(n) = A124353(n)/2.
From Colin Barker, Jul 12 2020: (Start)
G.f.: x*(3 - 8*x^2 - 4*x^3 + 3*x^4) / ((1 - x)^2*(1 - x - 2*x^2 - x^3)).
a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) + a(n-5) for n>5.
(End)
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MATHEMATICA
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LinearRecurrence[{3, -1, -2, 0, 1}, {3, 9, 16, 29, 56}, 40] (* Harvey P. Dale, Aug 06 2020 *)
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PROG
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(PARI) Vec(x*(3 - 8*x^2 - 4*x^3 + 3*x^4) / ((1 - x)^2*(1 - x - 2*x^2 - x^3)) + O(x^35)) \\ Colin Barker, Jul 12 2020
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CROSSREFS
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Sequence in context: A174440 A244475 A212870 * A257034 A232167 A058538
Adjacent sequences: A306444 A306445 A306446 * A306448 A306449 A306450
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein, May 04 2019
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STATUS
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approved
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