A003093 Number of planar 2-trees with n nodes. (Formerly M1977)

1, 2, 10, 83, 690, 6412, 61842, 617025, 6302725, 65619820, 693643860, 7425181257, 80326705270, 876832043840, 9645743783040, 106827450870525, 1190150414448795, 13329010510209790, 149976822229984908, 1694617702395672670, 19220402733369657820

Offset

3,2

Comments

Table 2 of Palmer and Read paper gives incorrect value a(10) = 457025. - Sean A. Irvine, Feb 12 2016

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=3..23.

Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.

E. M. Palmer and R. C. Read, On the number of plane 2-trees, J. Lond. Math. Soc., 6 (1973), 583-592.

E. M. Palmer and R. C. Read, On the number of plane 2-trees, J. Lond. Math. Soc., 6 (1973), 583-592. [Annotated and corrected scanned copy]

Index entries for sequences related to trees

Formula

G.f.: P(x) + (1/2) * x^2 * ((1 - T(x^2))^(-1) - 1) + (2/3) * x^3 * (1 - T(x^3))^(-2) where P(x) = Sum_{k>=1} ((k * (k - 1) * (5*k-10)! / (4*k-6)!) * x^k / k!) is the e.g.f. of A003092 and T(x) = Sum_{k>=1} (((5 * k - 2)!/ (4 * k - 1)!) * x^k / k!) is the e.g.f. of A120348. - Sean A. Irvine, Feb 12 2016

Crossrefs

Cf. A003092, A120348.

Sequence in context: A281547 A111265 A296667 * A006679 A050390 A298690

Adjacent sequences: A003090 A003091 A003092 * A003094 A003095 A003096

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(10) corrected and more terms from Sean A. Irvine, Feb 12 2016

Status

approved