0,3

Number of rooted loopless planar maps with n edges. E.g. there are a(2)=3 loopless planar maps with 2 edges: two rooted paths (.-.-.) and one digon (.=.). - Valery A. Liskovets (liskov(AT)im.bas-net.by), Sep 25 2003

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

Also the number of intervals (i.e. ordered pairs (x,y) such that x<=y) in the Tamari lattices or equivalently in the rotation lattices of binary trees. - Jean Pallo (Jean.Pallo(AT)u-bourgogne.fr), Sep 11 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).

Bender, E. A. and Wormald, N. C., The number of loopless planar maps, Discr. Math. 54:2 (1985), 235-237.

F. David, A model of random surfaces with nontrivial critical behavior, Nuclear Physics B, v. 257 (1985), 543-576.

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

Handbook of Combinatorics, North-Holland '95, p. 891.

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

W. T. Tutte, A census of planar triangulations, Canad. J. Math., 14 (1962), 21-38.

W. T. Tutte, A census of Hamiltonian polygons, Canad. J. Math., 14 (1962), 402-417.

W. T. Tutte, The enumerative theory of planar maps, in A Survey of Combinatorial Theory (J. N. Srivastava et al. eds.), pp. 437-448, North-Holland, Amsterdam, 1973.

Walsh, T. R. S. and Lehman, A. B., Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259.

C. Germain and J. Pallo, The number of coverings in four Catalan lattices, Intern. J. Computer Math., Vol. 61 (1996) pp. 19-28. (See p. 27.)

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

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

2(4n+1)! / (n+1)!(3n+2)! = binomial(4n+1, n+1) - 9*binomial(4n+1, n-1).

A000260 := n->2*(4*n-11)!/( (3*n-7)!*(n-2)!);

(PARI) a(n)=if(n<0, 0, 2*(4*n+1)!/(n+1)!/(3*n+2)!) /* Michael Somos Sep 07 2005 */

Cf. A000256, A027836.

Sequence in context: A042659 A054132 A047149 this_sequence A125279 A121954 A058307

Adjacent sequences: A000257 A000258 A000259 this_sequence A000261 A000262 A000263

nonn,nice,easy

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