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A306447 Number of (undirected) Hamiltonian cycles in the n-antiprism graph. 1
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; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Extended to a(1)-a(2) using the formula/recurrence.

LINKS

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).

FORMULA

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)

MATHEMATICA

LinearRecurrence[{3, -1, -2, 0, 1}, {3, 9, 16, 29, 56}, 40] (* Harvey P. Dale, Aug 06 2020 *)

PROG

(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

CROSSREFS

Sequence in context: A174440 A244475 A212870 * A257034 A232167 A058538

Adjacent sequences:  A306444 A306445 A306446 * A306448 A306449 A306450

KEYWORD

nonn,easy,changed

AUTHOR

Eric W. Weisstein, May 04 2019

STATUS

approved

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Last modified August 15 16:02 EDT 2020. Contains 336505 sequences. (Running on oeis4.)