%I A000257 M2927 N1175
%S A000257 1,1,3,12,56,288,1584,9152,54912,339456,2149888,13891584,91287552,
%T A000257 608583680,4107939840,28030648320,193100021760,1341536993280,
%U A000257 9390758952960,66182491668480,469294031831040,3346270487838720
%N A000257 Number of rooted bicubic maps: a(n)=(8n-4)a(n-1)/(n+2).
%C A000257 Number of rooted Eulerian planar maps with n edges. - Valery A. Liskovets 
               (liskov(AT)im.bas-net.by), Apr 07 2002
%C A000257 Number of indecomposable 1342-avoiding permutations of length n.
%C A000257 Also counts rooted planar 2-constellations with n digons. - Valery Liskovets 
               (liskov(AT)im.bas-net.by), Dec 01 2003
%C A000257 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
%C A000257 Number of intervals in Tamari lattices of size n (see Chapoton paper). 
               - Ralf Stephan, May 08 2007
%D A000257 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000257 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000257 E. A. Bender and E. R. Canfield The number of degree restricted maps 
               on the sphere. SIAM J. Discr. Math., 7 (1994), 9-15.
%D A000257 L. M. Koganov, V. A. Liskovets, T. R. S. Walsh, Total vertex enumeration 
               in rooted planar maps, Ars Combin. 54 (2000), 149-160.
%D A000257 Ph. Leroux, A simple symmetry generating operads related to rooted planar 
               m-ary trees and polygonal numbers, arXiv:math.CO/0512437.
%D A000257 Z. Li and Y. Liu, Chromatic sums of general maps on the sphere and the 
               projective plane, Discr. Math. 307 (2007), 78-87.
%D A000257 V. A. Liskovets and T. R. S. Walsh, Enumeration of Eulerian and unicursal 
               planar maps, Discr. Math., 282 (2004), 209-221.
%D A000257 W. T. Tutte, A census of planar maps, Canad. J. Math., 15 (1963), 249-271.
%D A000257 T. R. S. Walsh, Hypermaps versus bipartite maps. J. Combin. Th., B18 
               (1975), 155-163.
%H A000257 T. D. Noe, <a href="b000257.txt">Table of n, a(n) for n=0..200</a>
%H A000257 M. Bona, <a href="http://arXiv.org/abs/math.CO/9702223">[math/9702223] 
               Exact enumeration of 1342-avoiding permutations: A close link with 
               labeled trees and planar maps</a>
%H A000257 M. Bousquet-Melou, <a href="http://arXiv.org/abs/math.CO/0501266">Limit 
               laws for embedded trees</a>
%H A000257 M. Bousquet-Melou and G. Schaeffer, <a href="http://www.labri.fr/Perso/
               ~bousquet/Articles/Constellations/co.ps.gz">Enumeration of planar 
               constellations</a>, Adv. in Appl. Math. v.24 (2000), 337-368.
%H A000257 P. Di Francesco, O. Golinelli and E. Guitter, <a href="http://arXiv.org/
               abs/hep-th/9602025">Meanders and the Temperley-Lieb algebra</a> (See 
               Eq. C.1).
%H A000257 A. Mednykh and R. Nedela, <a href="http://garsia.math.yorku.ca/fpsac06/
               papers/9_ps_or_pdf.pdf">Counting unrooted hypermaps on closed orientable 
               surface</a>, 18th Intern. Conf. Formal Power Series & Algebr. Comb., 
               Jun 19, 2006, San Diego, California (USA).
%H A000257 F. Chapoton, <a href="http://arXiv.org/abs/math.CO/0602368">Sur le nombre 
               d'intervalles dans les treillis de Tamari</a>
%F A000257 3*2^(n-1)*C(n)/(n+2), C = Catalan (A000108).
%F A000257 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
%Y A000257 Cf. A069726.
%Y A000257 Equals 2^(n-2) * A007054(n), n>1.
%Y A000257 First row of array A102544.
%Y A000257 Sequence in context: A050147 A120921 A074533 this_sequence A027390 A009499 
               A009656
%Y A000257 Adjacent sequences: A000254 A000255 A000256 this_sequence A000258 A000259 
               A000260
%K A000257 nonn,easy,nice
%O A000257 0,3
%A A000257 N. J. A. Sloane (njas(AT)research.att.com).