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A137883
Number of (directed) Hamiltonian paths in the n-Möbius ladder graph.
0
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
Eric Weisstein's World of Mathematics, Hamiltonian Path
Eric Weisstein's World of Mathematics, Möbius Ladder
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Feb 20 2008
EXTENSIONS
More terms from Colin Barker, Apr 05 2013
STATUS
approved