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.
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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved