A104268 a(n) = 2*4^(n-1) - (3n-1)/(2n+2)*C(2n,n).

1, 3, 12, 51, 218, 926, 3902, 16323, 67866, 280746, 1156576, 4748398, 19439332, 79391708, 323584322, 1316578403, 5348814842, 21702312818, 87955584152, 356114261498, 1440568977932, 5822909703908, 23520345224732

Offset

1,2

Comments

Cardinality of the set of nesting-similarity classes.

Number of Lyngsø-Pedersen structures with n arcs [Saule et al., Theorem 1]. - Eric M. Schmidt, Sep 20 2017

Links

Table of n, a(n) for n=1..23.

M. Klazar, On identities concerning the numbers of crossings and nestings of two edges in matchings, arXiv:math/0503012 [math.CO], 2005.

Cédric Saule, Mireille Regnier, Jean-Marc Steyaert, Alain Denise, Counting RNA pseudoknotted structures (extended abstract), dmtcs:2834 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)

Formula

G.f.: C+z^2(2zC'+C)^2C, with C(z) the g.f. of the Catalan numbers.

G.f.: (x*(8*x+5*Sqrt[1-4 x]-9)-2*Sqrt[1-4 x]+2)/(2*(1-4*x)*x^2). [Harvey P. Dale, Oct 03 2011]

Conjecture: 2*(n+1)*a(n) +(-21*n+1)*a(n-1) +2*(36*n-43)*a(n-2) +40*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Jun 08 2016

Mathematica

Table[2 4^(n-1)-(3n-1)/(2n+2) Binomial[2n, n], {n, 30}] (* Harvey P. Dale, Oct 03 2011 *)

Crossrefs

Equals A006419(n-1) + A000108(n).

Sequence in context: A083314 A155179 A228770 * A081704 A166482 A007854

Adjacent sequences: A104265 A104266 A104267 * A104269 A104270 A104271

Keyword

nonn,easy

Author

Ralf Stephan, Apr 17 2005

Status

approved