A256330 Number of H&S Family matchings on n edges.

1, 3, 14, 84, 592, 4659, 39699, 359004

Offset

1,2

Comments

The H&S Family of matchings is the family of matchings that can be drawn in the plane without crossings.

Jay Pantone has computed the first 1500 terms and has a conjectured g.f. - N. J. A. Sloane, Oct 06 2016

Links

Table of n, a(n) for n=1..8.

Michael Albert and Mireille Bousquet-Mélou. Permutations sortable by two stacks in parallel and quarter plane walks, European Journal of Combinatorics 43 (2015): 131-164. Also arXiv:1312.4487 [math.CO], 2013-2014.

C. Haslinger and P. F. Stadler, RNA structures with pseudo-notes: Graph-theoretical, combinatorial, and statistical properties, Bulletin of Mathematical Biology 61 (1999), 437-467.

Aziza Jefferson, The Substitution Decomposition of Matchings and RNA Secondary Structures, PhD Thesis, University of Florida, 2015.

Jay Pantone, Approximate Asymptotic Analysis of Combinatorial Sequences, Experimental Math Seminar, Rutgers University, Oct 06 2016.

Example

a(5)= 592; in canonical sequence form the two 3-noncrossing matchings it does not include are 1231435425 and 1234254153.

Crossrefs

Sequence in context: A359335 A074535 A256337 * A190761 A005700 A220911

Adjacent sequences: A256327 A256328 A256329 * A256331 A256332 A256333

Keyword

nonn,more

Author

Aziza Jefferson, Mar 25 2015

Status

approved