0,2

Number of nonisomorphic unrooted unicursal planar maps with n+2 edges and exactly one vertex of valency 1 (unicursal means that exactly two vertices are of odd valency). - Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 07 2002

Total number of vertices in rooted Eulerian planar maps with n+1 edges.

Half the number of ways to dog-ear every page of an n+1 page book. - Ron Hardin (rhh(AT)cadence.com), Jun 21 2002

Convolution of A052701(n+1) with itself.

Number of Motzkin lattice paths with weights: 1 for up step, 4 for level step and 4 for down step. - Wen-jin Woan (wwoan(AT)howard.edu), Oct 24 2004

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

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

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

Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 652

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

a(n)=(2^n)*binomial(2*n+3, n+1)/(2*n+3) - Len Smiley (smiley(AT)math.uaa.alaska.edu)

G.f.: (1-4x-sqrt(1-8x))/(8x^2) = C(2x)^2 where C(x) is g.f. for Catalan numbers, A000108.

(PARI) a(n)=if(n<0, 0, 2^n*(2*n+2)!/(n+1)!/(n+2)!)

Cf. A069724, A069725. a(n)=A052701(n+2)/2.

Third row of array A102539.

Column of array A073165.

Cf. A052701.

Sequence in context: A081335 A136783 A080609 this_sequence A081085 A108447 A028475

Adjacent sequences: A003642 A003643 A003644 this_sequence A003646 A003647 A003648

nonn

njas