cp's OEIS Frontend

A158525 Number of connected spanning subgraphs and number of forests of the wheel graph W_n.

%I A158525 #21 Apr 15 2025 13:04:22
%S A158525 38,134,462,1582,5406,18462,63038,215230,734846,2508926,8566014,
%T A158525 29246206,99852798,340918782,1163969534,3974040574,13568223230,
%U A158525 46324811774,158162800638,540001579006,1843680714750,6294719700990,21491517374462,73376630095870,250523485634558
%N A158525 Number of connected spanning subgraphs and number of forests of the wheel graph W_n.
%C A158525 The wheel graph W_n has n vertices and 2n-2 edges. A single vertex is connected to all vertices of an (n-1)-cycle.
%H A158525 Vincenzo Librandi, <a href="/A158525/b158525.txt">Table of n, a(n) for n = 4..1000</a>
%H A158525 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WheelGraph.html">Wheel Graph</a>
%H A158525 Wikipedia, <a href="https://en.wikipedia.org/wiki/Wheel_graph">Wheel graph</a>
%H A158525 Yaohui Zhu, Kaiming Sun, Zhengdong Luo, and Lingfeng Wang, <a href="https://doi.org/10.1609/aaai.v39i2.32162">Progressive Self-Learning for Domain Adaptation on Symbolic Regression of Integer Sequences</a>, Proc. 39th AAAI Conf. Artif. Intel. (2025) Vol. 39, No. 1, 1692-1699. See p. 1698.
%H A158525 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,2).
%F A158525 G.f.: (38-56*x+20*x^2)*x^4 / (6*x^2+1-5*x-2*x^3).
%F A158525 a(n) = 2 * A035344(n-2).
%p A158525 a:= n-> `if`(n<4, 0, (Matrix([[5, 1, 0], [ -6, 0, 1], [2, 0, 0]])^n)[3, 2]): seq(a(n), n=4..30);
%t A158525 CoefficientList[Series[((1 / x^4) (38 - 56 x + 20 x^2) x^4 / (6 x^2 + 1 - 5 x - 2 x^3)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 06 2013 *)
%Y A158525 Cf. A035344.
%K A158525 nonn,easy
%O A158525 4,1
%A A158525 _Alois P. Heinz_, Mar 20 2009