A097999 Number of 2-connected outerplanar graphs on n labeled nodes.

1, 9, 132, 2700, 70920, 2275560, 86264640, 3772681920, 186972105600, 10355595465600, 633892275878400, 42495895579737600, 3096545573029708800, 243680880958010496000, 20596410256606119936000, 1860881636529774802944000, 178975197401013144907776000, 18256461815785805072068608000

Offset

3,2

References

Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 424, see B(x).

Links

Andrew Howroyd, Table of n, a(n) for n = 3..200

Bodirsky, M., Giménez, O., Kang, M., & Noy, M., The asymptotic number of outerplanar graphs and series-parallel graphs, in Proceedings of European Conference on Combinatorics, Graph Theory, and Applications (EuroComb05), DMTCS Proceedings Volume AE (pp. 383-388). [Cached copy, with permission]

M. Bodirsky and M. Kang, The asymptotic number of outerplanar graphs. [Only the abstract has been archived]

M. Drmota, O. Gimenez, Marc Noy, Vertices of given degree in series-parallel graphs, Random Struct. Algor. 36 (3) (2010), 251-371, Lemma 2.3

Steven R. Finch, Planar graph growth constants.

Formula

Recurrence known, see Bodirsky and Kang.

E.g.f.: (-3+2*x-3*x^2)/16+(3-x)*sqrt(1-6*x+x^2)/16+log((3-x-sqrt(1-6*x+x^2))/2)/2. - Vladeta Jovovic, Jun 26 2007

a(n) ~ 2^(-5/2) * sqrt(3*sqrt(2)-4) * (1+sqrt(2))^(2*n-2) * n^(n-2) / exp(n). - Vaclav Kotesovec, Nov 05 2016

Mathematica

offset = 3; terms = 15; egf = (-3 + 2*x - 3*x^2)/16 + (3 - x)*(Sqrt[1 - 6*x + x^2]/16) + Log[(3 - x - Sqrt[1 - 6*x + x^2])/2]/2; Drop[ CoefficientList[ egf + O[x]^(terms + offset), x]*Range[0, terms + offset - 1]!, offset] (* Jean-François Alcover, Nov 05 2016, after Vladeta Jovovic *)

Prog

(PARI) seq(n)={Vec(serlaplace(intformal((1 + 5*x - sqrt(1 - 6*x + x^2 + O(x^n)))/8 - x)))} \\ Andrew Howroyd, Feb 12 2021

Crossrefs

Cf. A097998, A098000.

Sequence in context: A296318 A167253 A366017 * A089547 A110273 A082760

Adjacent sequences: A097996 A097997 A097998 * A098000 A098001 A098002

Keyword

nonn

Author

Steven Finch, Sep 08 2004

Extensions

Terms a(18) and beyond from Andrew Howroyd, Feb 12 2021

Status

approved