0,2

Total number of vertices in rooted planar maps with n edges.

Number of blossom trees with n inner vertices.

The number of rooted n-edge maps in the plane (planar with a distinguished outside face). - Valery A. Liskovets (liskov(AT)im.bas-net.by), Mar 17 2005

Hankel transform is 3^(n+n^2)=A053764(n+1). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 10 2007

L. M. Koganov, V. A. Liskovets, T. R. S. Walsh, Total vertex enumeration in rooted planar maps, Ars Combin. 54 (2000), 149-160.

V. A. Liskovets, A pattern of asymptotic vertex valency distributions in planar maps. J. Combin. Th., B75 (1999), 116-133.

V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.

T. D. Noe, Table of n, a(n) for n=0..100

M. Bousquet-Melou, Limit laws for embedded trees

G. 't Hooft, Counting planar diagrams with various restrictions, Nucl. Phys. B538 (1999), 389-410.

V. A. Liskovets and T. R. Walsh, Counting unrooted maps on the plane, Advances in Applied Math., 36, No.4 (2006), 364-387.

G. Schaeffer and P. Zinn-Justin, On the asymptotic number of plane curves and alternating knots

G.f.: 2/(1+sqrt(1-12x)).

With offset 1 : a(1)=1, a(n)=3*sum(i=1, n-1, a(i)*a(n-i)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 16 2004

G.f.: c(3*x) with c(x) the o.g.f. of A000108 (Catalan).

InverseSeries[Series[y-3*y^2, {y, 0, 24}], x] (* then A(x)=y(x)/x *) - Len Smiley Apr 07 2000

Cf. A000108, A025226.

Limit of array A102994.

Sequence in context: A074545 A095776 A114178 this_sequence A151383 A118970 A003122

Adjacent sequences: A005156 A005157 A005158 this_sequence A005160 A005161 A005162

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com), Valery A. Liskovets (liskov(AT)im.bas-net.by)