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%I #16 Feb 28 2023 09:12:30
%S 38,134,462,1582,5406,18462,63038,215230,734846,2508926,8566014,
%T 29246206,99852798,340918782,1163969534,3974040574,13568223230,
%U 46324811774,158162800638,540001579006,1843680714750,6294719700990,21491517374462,73376630095870,250523485634558
%N Number of connected spanning subgraphs and number of forests of the wheel graph W_n.
%C 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 Vincenzo Librandi, <a href="/A158525/b158525.txt">Table of n, a(n) for n = 4..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WheelGraph.html">Wheel Graph</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Wheel_graph">Wheel graph</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,2).
%F G.f.: (38-56*x+20*x^2)*x^4 / (6*x^2+1-5*x-2*x^3).
%F a(n) = 2 * A035344(n-2).
%p 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 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 Cf. A035344.
%K nonn,easy
%O 4,1
%A _Alois P. Heinz_, Mar 20 2009
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