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A020873 a(n) = number of cycles in Moebius ladder M_n. 16
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

For n >= 2, a(n+1) is the number of connected induced (non-null) subgraphs of the n-wheel graph. - Giovanni Resta, May 04 2017

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).

FORMULA

a(n) = 2^n + n^2 - n + 1.

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). - R. J. Mathar, May 31 2010

MATHEMATICA

Table[2^n+n^2-n+1, {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, May 07 2010 *)

PROG

(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

CROSSREFS

Sequence in context: A001276 A006884 A074742 * A049958 A177487 A153010

Adjacent sequences:  A020870 A020871 A020872 * A020874 A020875 A020876

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 23 13:55 EDT 2017. Contains 292358 sequences.