0,1

The number of rooted non-separable planar maps with n edges. - Valery A. Liskovets (liskov(AT)im.bas-net.by), Mar 17 2005

The shifted sequence starting with a(1): Number of quadrangular dissections of a square, counted by the number of vertices. Rooted, non-separable planar maps with no multiple edges, in which each non-root face has degree 4.

Number of left ternary trees having n nodes (n>=1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 23 2006

W. G. Brown, Enumeration of non-separable planar maps, Canad. J. Math., 15:3 (1963), 526-545.

A. Del Lungo, F. Del Ristoro and J.-G. Penaud, Left ternary trees and non-separable rooted planar maps, Theor. Comp. Sci., 233, 2000, 201-215.

J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 714.

O. Guibert, Stack words, ..., Discr. Math., 210 (2000), 71-85.

W. F. Lunnon, Counting polyominoes, pp. 347-372 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 6.41.

W. T. Tutte, A census of planar maps, Canad. J. Math., 15 (1963), 249-271.

J. West, Sorting twice through a stack. Conference on Formal Power Series and Algebraic Combinatorics (Bordeaux, 1991). Theoret. Comput. Sci. 117 (1993), no. 1-2, 303-313.

D. Zeilberger, A proof of Julian West's conjecture ..., Discrete Math., 102 (1992), 85-93.

T. D. Noe, Table of n, a(n) for n=0..200

M. Bousqet-Melou and A. Jehanne, Polynomial equations with one catalytic variable, algebraic series and map enumeration

I. Gessel and G. Xin, The generating function of ternary trees and continued fractions

P. Zinn-Justin and J.-B. Zuber, Matrix integrals and the generation and counting of virtual tangles and links, p. 11.

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 713

2*C(3n, 2n+1)/(n(n+1)), or 2*(3*n)!/((2*n+1)!*((n+1)!)).

Using Stirling's formula in A000142 it easy to get the asymptotic expression a(n) ~ (27/4)^n / (sqrt(Pi*n / 3) * (2n + 1) * (n + 1)). - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 13 2001

G.f. A(z) = 2 + zB(z), where B(z) = 1 - 8z + 2z(5-6z)B - 2z^2(1+3z)B^2 - z^4B^3.

A000139 := n->2*(3*n)!/((2*n+1)!*((n+1)!)); [seq(f(i), i=0..30)];

Cf. A000142.

Cf. A000309, A006335, A004677.

Adjacent sequences: A000136 A000137 A000138 this_sequence A000140 A000141 A000142

Sequence in context: A032085 A032163 A038078 this_sequence A114572 A052621 A131057

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).