A020875 - OEIS

%I #30 May 07 2019 15:09:35

%S 0,4,12,36,72,140,228,364,528,756,1020,1364,1752,2236,2772,3420,4128,

%T 4964,5868,6916,8040,9324,10692,12236,13872,15700,17628,19764,22008,

%U 24476,27060,29884,32832,36036,39372

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

%H Vincenzo Librandi, <a href="/A020875/b020875.txt">Table of n, a(n) for n = 0..1000</a>

%H J. P. McSorley, <a href="https://doi.org/10.1016/S0012-365X(97)00086-1">Counting structures in the Möbius ladder</a>, Discrete Math., 184 (1998), 137-164.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Möbius Ladder</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).

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

%F G.f.: 4*x*(x^2+1)*(x^2+x+1) / ((x-1)^4*(x+1)^2). - _Colin Barker_, Apr 05 2013

%p 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);

%t 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 *)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.