A158525 Number of connected spanning subgraphs and number of forests of the wheel graph W_n.
38, 134, 462, 1582, 5406, 18462, 63038, 215230, 734846, 2508926, 8566014, 29246206, 99852798, 340918782, 1163969534, 3974040574, 13568223230, 46324811774, 158162800638, 540001579006, 1843680714750, 6294719700990, 21491517374462, 73376630095870, 250523485634558
Offset: 4
Links
- Vincenzo Librandi, Table of n, a(n) for n = 4..1000
- Eric Weisstein's World of Mathematics, Wheel Graph
- Wikipedia, Wheel graph
- Yaohui Zhu, Kaiming Sun, Zhengdong Luo, and Lingfeng Wang, Progressive Self-Learning for Domain Adaptation on Symbolic Regression of Integer Sequences, Proc. 39th AAAI Conf. Artif. Intel. (2025) Vol. 39, No. 1, 1692-1699. See p. 1698.
- Index entries for linear recurrences with constant coefficients, signature (5,-6,2).
Crossrefs
Cf. A035344.
Programs
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Maple
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);
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Mathematica
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 *)
Formula
G.f.: (38-56*x+20*x^2)*x^4 / (6*x^2+1-5*x-2*x^3).
a(n) = 2 * A035344(n-2).
Comments