A004300 - OEIS

%I M1758 #38 May 22 2024 12:56:22

%S 1,1,2,7,22,96,380,1853,8510,44940,229836,1296410,7211116,43096912,

%T 256874200,1617413773,10226972110,67542201972,449809389740,

%U 3104409032126

%N Number of symmetric irreducible diagrams with 2n nodes.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Jonathan Burns, <a href="http://shell.cas.usf.edu/~saito/DNAweb/SimpleAssemblyTable.txt">Assembly Graph Words - Single Transverse Component (Counts)</a>.

%H Jonathan Burns, Egor Dolzhenko, Natasa Jonoska, Tilahun Muche, and Masahico Saito, <a href="https://doi.org/10.1016/j.dam.2013.01.003">Four-Regular Graphs with Rigid Vertices Associated to DNA Recombination</a>, Discrete Applied Mathematics, Volume 161, Issues 10-11, July 2013, Pages 1378-1394; and <a href="https://web.archive.org/web/20191206080922/http://jtburns.myweb.usf.edu:80/assembly/papers/Graphs_and_DNA_Recomb_2011.pdf">preprint</a>, 2011.

%H Jonathan Burns and Tilahun Muche, <a href="http://arxiv.org/abs/1105.2926">Counting Irreducible Double Occurrence Words</a>, arXiv preprint arXiv:1105.2926 [math.CO], 2011.

%H Martin Klazar, <a href="https://doi.org/10.1016/S0196-8858(02)00528-6">Non-P-recursiveness of numbers of matchings or linear chord diagrams with many crossings</a>, Advances in Appl. Math., Vol. 30 (2003), pp. 126-136.

%H Paul R. Stein, <a href="https://doi.org/10.1016/0097-3165(78)90065-1">On a class of linked diagrams, I. Enumeration</a>, J. Combin. Theory, A 24 (1978), 357-366.

%H Paul R. Stein and C. J. Everett, <a href="https://doi.org/10.1016/0012-365X(78)90162-0">On a class of linked diagrams, II. Asymptotics</a>, Discrete Math., 21 (1978), 309-318.

%Y Cf. A000699.

%K nonn,nice,easy

%O 1,3

%A _N. J. A. Sloane_