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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
OFFSET
0,2
LINKS
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
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 A374906 A357061
KEYWORD
nonn,easy
AUTHOR
STATUS
approved