A020873 a(n) is number of cycles in Moebius ladder M_n.
2, 3, 7, 15, 29, 53, 95, 171, 313, 585, 1115, 2159, 4229, 8349, 16567, 32979, 65777, 131345, 262451, 524631, 1048957, 2097573, 4194767, 8389115, 16777769, 33555033, 67109515, 134218431, 268436213, 536871725, 1073742695, 2147484579, 4294968289, 8589935649
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- J. P. McSorley, Counting structures in the Moebius ladder, Discrete Math., 184 (1998), 137-164.
- Eric Weisstein's World of Mathematics, Connected Graph
- Eric Weisstein's World of Mathematics, Graph Cycle
- Eric Weisstein's World of Mathematics, Möbius Ladder
- Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
- Eric Weisstein's World of Mathematics, Wheel Graph
- Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).
Programs
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Mathematica
Table[2^n+n^2-n+1,{n,0,5!}] (* Vladimir Joseph Stephan Orlovsky, May 07 2010 *) -
PARI
Vec((2-7*x+10*x^2-7*x^3) / ((2*x-1)*(x-1)^3) + O(x^50)) \\ Colin Barker, Aug 01 2015
Formula
a(n) = 2^n + n^2 - n + 1.
From R. J. Mathar, May 31 2010: (Start)
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).
G.f.: (2 - 7*x + 10*x^2 - 7*x^3)/((2*x - 1)*(x - 1)^3). (End)
E.g.f.: exp(x)*(1 + exp(x) + x^2). - Stefano Spezia, Aug 25 2022
Comments