This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A256330 #44 Jun 17 2025 03:15:11 %S A256330 1,3,14,84,592,4659,39699,359004,3399164,33378417,337584612, %T A256330 3498553682,37006524557,398312230440,4351822041763,48169486233388, %U A256330 539303075161814,6099303431601708,69604032964928589,800737747350839332,9279033826462097649,108236883894562489628 %N A256330 Number of H&S Family matchings on n edges. %C A256330 The H&S Family of matchings is the family of matchings that can be drawn in the plane without crossings. %C A256330 Jay Pantone has computed the first 1500 terms and has a conjectured g.f. - _N. J. A. Sloane_, Oct 06 2016 %C A256330 Consider the graph whose vertices are the arcs of a matching, where two vertices are connected if the corresponding arcs cannot be drawn on the same side without crossing. Matchings, where the graph obtained this way is connected, are in bijection with 3-edge-connected rooted cubic maps with 2n nodes and a distinguished Hamiltonian cycle (cf. A000264). - _Ludovic Schwob_, Jun 17 2025 %H A256330 Ludovic Schwob, <a href="/A256330/b256330.txt">Table of n, a(n) for n = 1..200</a> %H A256330 Michael Albert and Mireille Bousquet-Mélou, <a href="http://arxiv.org/abs/1312.4487">Permutations sortable by two stacks in parallel and quarter plane walks</a>, European Journal of Combinatorics 43 (2015): 131-164. Also arXiv:1312.4487 [math.CO], 2013-2014. %H A256330 C. Haslinger and P. F. Stadler, <a href="http://dx.doi.org/10.1006/bulm.1998.0085">RNA structures with pseudo-notes: Graph-theoretical, combinatorial, and statistical properties</a>, Bulletin of Mathematical Biology 61 (1999), 437-467. %H A256330 Aziza Jefferson, <a href="http://ufdc.ufl.edu/UFE0047620">The Substitution Decomposition of Matchings and RNA Secondary Structures</a>, PhD Thesis, University of Florida, 2015. %H A256330 Jay Pantone, <a href="https://vimeo.com/185888450">Approximate Asymptotic Analysis of Combinatorial Sequences</a>, Experimental Math Seminar, Rutgers University, Oct 06 2016. %e A256330 a(5)= 592; in canonical sequence form the two 3-noncrossing matchings it does not include are 1231435425 and 1234254153. %Y A256330 Cf. A000264. %K A256330 nonn %O A256330 1,2 %A A256330 _Aziza Jefferson_, Mar 25 2015