A137883 Number of (directed) Hamiltonian paths in the n-Möbius ladder graph.

72, 144, 280, 456, 728, 1056, 1512, 2040, 2728, 3504, 4472, 5544, 6840, 8256, 9928, 11736, 13832, 16080, 18648, 21384, 24472, 27744, 31400, 35256, 39528, 44016, 48952, 54120, 59768, 65664, 72072, 78744, 85960, 93456, 101528, 109896, 118872, 128160, 138088

Offset

3,1

Links

Table of n, a(n) for n=3..41.

Eric Weisstein's World of Mathematics, Hamiltonian Path

Eric Weisstein's World of Mathematics, Möbius Ladder

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Formula

a(n) = (-1)^n*n*(-1 + (-1)^n*(5 + 2*n^2)). - Eric W. Weisstein, Dec 16 2013

G.f.: -8*x^3*(3*x^5-5*x^4-5*x^3+10*x^2-9) / ((x-1)^4*(x+1)^2). - Colin Barker, Apr 05 2013

Mathematica

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {72, 144, 280, 456, 728, 1056}, 40] (* Vincenzo Librandi, Feb 22 2016 *)

Prog

(PARI) Vec(-8*x^3*(3*x^5-5*x^4-5*x^3+10*x^2-9)/((x-1)^4*(x+1)^2) + O(x^100)) \\ Colin Barker, Aug 02 2015
(Magma) [(-1)^n*n*(-1+(-1)^n*(5+2*n^2)): n in [3..45]]; // Vincenzo Librandi, Feb 22 2016

Crossrefs

Sequence in context: A369334 A060661 A050495 * A173728 A173547 A173727

Adjacent sequences: A137880 A137881 A137882 * A137884 A137885 A137886

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 20 2008

Extensions

More terms from Colin Barker, Apr 05 2013

Status

approved