0,3

Number of rooted Eulerian planar maps with n edges. - Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 07 2002

Number of indecomposable 1342-avoiding permutations of length n.

Also counts rooted planar 2-constellations with n digons. - Valery Liskovets (liskov(AT)im.bas-net.by), Dec 01 2003

a(n) is also the number of rooted planar hypermaps with n darts (darts are semi-edges in the particular case of ordinary maps). - Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 13 2006

Number of intervals in Tamari lattices of size n (see Chapoton paper). - Ralf Stephan, May 08 2007

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

E. A. Bender and E. R. Canfield The number of degree restricted maps on the sphere. SIAM J. Discr. Math., 7 (1994), 9-15.

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

Ph. Leroux, A simple symmetry generating operads related to rooted planar m-ary trees and polygonal numbers, arXiv:math.CO/0512437.

Z. Li and Y. Liu, Chromatic sums of general maps on the sphere and the projective plane, Discr. Math. 307 (2007), 78-87.

V. A. Liskovets and T. R. S. Walsh, Enumeration of Eulerian and unicursal planar maps, Discr. Math., 282 (2004), 209-221.

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

T. R. S. Walsh, Hypermaps versus bipartite maps. J. Combin. Th., B18 (1975), 155-163.

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

M. Bona, [math/9702223] Exact enumeration of 1342-avoiding permutations: A close link with labeled trees and planar maps

M. Bousquet-Melou, Limit laws for embedded trees

M. Bousquet-Melou and G. Schaeffer, Enumeration of planar constellations, Adv. in Appl. Math. v.24 (2000), 337-368.

P. Di Francesco, O. Golinelli and E. Guitter, Meanders and the Temperley-Lieb algebra (See Eq. C.1).

A. Mednykh and R. Nedela, Counting unrooted hypermaps on closed orientable surface, 18th Intern. Conf. Formal Power Series & Algebr. Comb., Jun 19, 2006, San Diego, California (USA).

F. Chapoton, Sur le nombre d'intervalles dans les treillis de Tamari

3*2^(n-1)*C(n)/(n+2), C = Catalan (A000108).

O.g.f.: (1/8) * ( -(1-8*x)^(1/2) + 16*(1-8*x)^(1/2)*x+1-8*x ) / ((1-8*x)^(1/2)*x*(1+(1-8*x)^(1/2))), e.g.f.: (1/8) * exp(4*x)*(8*BesselI(0, 4*x)*x-BesselI(1, 4*x)-8*BesselI(1, 4*x)*x)/x. - Karol A. Penson (penson(AT)lptl.jussieu.fr), Jun 04 2004

Cf. A069726.

Equals 2^(n-2) * A007054(n), n>1.

First row of array A102544.

Sequence in context: A050147 A120921 A074533 this_sequence A027390 A009499 A009656

Adjacent sequences: A000254 A000255 A000256 this_sequence A000258 A000259 A000260

nonn,easy,nice

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