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A306447 Number of (undirected) Hamiltonian cycles in the n-antiprism graph. 1

%I #30 Aug 06 2020 18:59:57

%S 3,9,16,29,56,110,225,469,991,2110,4511,9666,20736,44511,95575,205253,

%T 440828,946817,2033628,4367986,9381949,20151433,43283195,92967882,

%U 199685571,428904390,921243268,1978737467,4250128235,9128846273,19607840040,42115660645

%N Number of (undirected) Hamiltonian cycles in the n-antiprism graph.

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

%H Colin Barker, <a href="/A306447/b306447.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AntiprismGraph.html">Antiprism Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-2,0,1).

%F a(n) = A124353(n)/2.

%F From _Colin Barker_, Jul 12 2020: (Start)

%F G.f.: x*(3 - 8*x^2 - 4*x^3 + 3*x^4) / ((1 - x)^2*(1 - x - 2*x^2 - x^3)).

%F a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) + a(n-5) for n>5.

%F (End)

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

%o (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

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, May 04 2019

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)