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A020875 Number of (undirected) Hamiltonian paths in n-Moebius ladder. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A190072 A063810

Adjacent sequences:  A020872 A020873 A020874 * A020876 A020877 A020878

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 25 12:16 EDT 2021. Contains 347654 sequences. (Running on oeis4.)