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 A256330 Number of H&S Family matchings on n edges. 2
 1, 3, 14, 84, 592, 4659, 39699, 359004 (list; graph; refs; listen; history; text; internal format)
 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 REFERENCES A. Jefferson, The Substitution Decomposition of Matchings and RNA Secondary Structures, Ph. D. Dissertation, Univ. of Florida, Math., 2015. Jay Pantone, Approximate Asymptotic Analysis of Combinatorial Sequences, Experimental Math Seminar, Rutgers University, Oct 06 2016. [Talk will soon be posted on Vimeo] LINKS Albert, Michael, and Mireille Bousquet-MÃ©lou. "Permutations sortable by two stacks in parallel and quarter plane walks, European Journal of Combinatorics 43 (2015): 131-164. Also arXiv:1312.4487 (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. 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: A154757 A074535 A256337 * A190761 A005700 A220911 Adjacent sequences:  A256327 A256328 A256329 * A256331 A256332 A256333 KEYWORD nonn,more AUTHOR Aziza Jefferson, Mar 25 2015 STATUS approved

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Last modified April 24 12:01 EDT 2019. Contains 322429 sequences. (Running on oeis4.)