A308136 Number of (undirected) Hamiltonian paths in the 2n-crossed prism graph.

72, 288, 960, 2880, 8064, 21504, 55296, 138240, 337920, 811008, 1916928, 4472832, 10321920, 23592960, 53477376, 120324096, 268959744, 597688320, 1321205760, 2906652672, 6366953472, 13891534848, 30198988800, 65431142400, 141331267584, 304405807104

Offset

2,1

Links

Colin Barker, Table of n, a(n) for n = 2..1000

Eric Weisstein's World of Mathematics, Crossed Prism Graph

Eric Weisstein's World of Mathematics, Hamiltonian Path

Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

Formula

a(n) = A137885(n)/2.

From Colin Barker, Jul 19 2019: (Start)

G.f.: 24*x^2*(3 - 6*x + 4*x^2) / (1 - 2*x)^3.

a(n) = 3*2^n*n*(1+n).

a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n>4.

(End)

Prog

(PARI) Vec(24*x^2*(3 - 6*x + 4*x^2) / (1 - 2*x)^3 + O(x^30)) \\ Colin Barker, Jul 19 2019

Crossrefs

Cf. A137885.

Sequence in context: A004007 A279272 A173546 * A242534 A277430 A277991

Adjacent sequences: A308133 A308134 A308135 * A308137 A308138 A308139

Keyword

nonn,easy

Author

Eric W. Weisstein, May 14 2019

Status

approved