A124349 Numbers of directed Hamiltonian cycles on the n-prism graph.

6, 12, 10, 16, 14, 20, 18, 24, 22, 28, 26, 32, 30, 36, 34, 40, 38, 44, 42, 48, 46, 52, 50, 56, 54, 60, 58, 64, 62, 68, 66, 72, 70, 76, 74, 80, 78, 84, 82, 88, 86, 92, 90, 96, 94, 100, 98, 104, 102, 108, 106, 112, 110, 116, 114, 120, 118, 124, 122, 128, 126, 132, 130

Offset

3,1

Links

Table of n, a(n) for n=3..65.

Eric Weisstein's World of Mathematics, Hamiltonian Cycle.

Eric Weisstein's World of Mathematics, Prism Graph.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = 2*n + (1-(n mod 2))*4.

From Colin Barker, Aug 22 2012: (Start)

a(n) = a(n-1)+a(n-2)-a(n-3).

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

a(n) = 2*A014681(n+1). - R. J. Mathar, Jan 25 2016

E.g.f.: 2*(2 + x)*cosh(x) + 2*x*sinh(x) - 2*(2 + x + 2*x^2). - Stefano Spezia, Jan 28 2024

Maple

seq( 2*n + (1-(n mod 2))*4, n=3..100); # Robert Israel, Mar 14 2016

Mathematica

Table[2 n + (1 - Mod[n, 2]) 4, {n, 3, 100}] (* Vincenzo Librandi, Jan 26 2016 *)

Prog

(Magma) [2*n+(1-(n mod 2))*4: n in [3..80]]; // Vincenzo Librandi, Jan 26 2016
(PARI) Vec(2*x^3*(3+3*x-4*x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ Altug Alkan, Mar 14 2016

Crossrefs

Cf. A014681, A124350, A270273.

Sequence in context: A279606 A352482 A164378 * A360719 A365787 A315566

Adjacent sequences: A124346 A124347 A124348 * A124350 A124351 A124352

Keyword

nonn,easy

Author

Eric W. Weisstein, Oct 26 2006

Extensions

Name clarified by Andrew Howroyd, Mar 14 2016

Status

approved