cp's OEIS Frontend

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.

A118814 Number of 'tree-like curves' with n intersection points.

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%I A118814 #22 Aug 15 2025 09:10:29
%S A118814 1,2,5,18,70,323,1683,9690,59917,388894,2606742,17869870,124516636,
%T A118814 878591340
%N A118814 Number of 'tree-like curves' with n intersection points.
%C A118814 The objects being enumerated are a subset of those enumerated by A008983. The restriction involved is that the Gauss diagram (or chord diagram) has no intersecting chords.
%D A118814 V. I. Arnold, Topological Invariants of plane curves and caustics, AMS, 1994, page 12.
%H A118814 Andrei Zabolotskii, <a href="https://github.com/colt-browning/closed_curves">closed_curves</a> - a program computing the sequence (2025).
%e A118814 The first 3 entries are the same as A008983 because, for less than 3 intersection points, all curves are tree-like. For 3 intersection points there are only 2 curves that are not tree-like. They appear as the 4th and 15th entries in the table for n=3, on page 14 of Arnold's book.
%Y A118814 Cf. A008983.
%K A118814 nonn,more
%O A118814 0,2
%A A118814 _Moshe Shmuel Newman_, May 23 2006
%E A118814 a(5)-a(11) from _Andrei Zabolotskii_, Jan 16 2025
%E A118814 a(12)-a(13) from _Andrei Zabolotskii_, Aug 15 2025