A020875 Number of (undirected) Hamiltonian paths in n-Moebius ladder.

0, 4, 12, 36, 72, 140, 228, 364, 528, 756, 1020, 1364, 1752, 2236, 2772, 3420, 4128, 4964, 5868, 6916, 8040, 9324, 10692, 12236, 13872, 15700, 17628, 19764, 22008, 24476, 27060, 29884, 32832, 36036, 39372

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

J. P. McSorley, Counting structures in the Möbius ladder, Discrete Math., 184 (1998), 137-164.

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

If n is even, a(n) = n^3+2*n, else a(n) = n^3+3*n.

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

Maple

A020875 := proc(n) if n mod 2 = 0 then return n^3+2*n; else return n^3+3*n; end if end proc: seq(A020875(n), n=0..50);

Mathematica

CoefficientList[Series[4 x (x^2 + 1) (x^2 + x + 1)/((x - 1)^4 (x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 16 2013 *)

Crossrefs

Sequence in context: A300553 A062858 A095735 * A307182 A357061 A190072

Adjacent sequences: A020872 A020873 A020874 * A020876 A020877 A020878

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved