|
%I #43 Aug 25 2022 16:31:22
%S 2,3,7,15,29,53,95,171,313,585,1115,2159,4229,8349,16567,32979,65777,
%T 131345,262451,524631,1048957,2097573,4194767,8389115,16777769,
%U 33555033,67109515,134218431,268436213,536871725,1073742695,2147484579,4294968289,8589935649
%N a(n) is number of cycles in Moebius ladder M_n.
%C 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
%H Colin Barker, <a href="/A020873/b020873.txt">Table of n, a(n) for n = 0..1000</a>
%H J. P. McSorley, <a href="http://dx.doi.org/10.1016/S0012-365X(97)00086-1">Counting structures in the Moebius ladder</a>, Discrete Math., 184 (1998), 137-164.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Möbius Ladder</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WheelGraph.html">Wheel Graph</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F a(n) = 2^n + n^2 - n + 1.
%F From _R. J. Mathar_, May 31 2010: (Start)
%F a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).
%F G.f.: (2 - 7*x + 10*x^2 - 7*x^3)/((2*x - 1)*(x - 1)^3). (End)
%F E.g.f.: exp(x)*(1 + exp(x) + x^2). - _Stefano Spezia_, Aug 25 2022
%t Table[2^n+n^2-n+1,{n,0,5!}] (* _Vladimir Joseph Stephan Orlovsky_, May 07 2010 *)
%o (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
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
|
