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 A333249 #19 Feb 15 2023 13:45:49 %S A333249 1,1,2,7,25,99,415,1849,8368,38712,181111,856833,4085025,19612082 %N A333249 Number of one-sided Tangles of size n. %C A333249 a(n) is the number of one-sided Tangles (smooth simple closed curves piecewise-defined by quadrants of circles) which have a dual graph containing n edges, or equivalently, enclose an area of (4*n + Pi)*r^2, where 1/r is the curvature. By 'one-sided', we mean that we allow rotations but not reflections. %C A333249 Dual graphs of Tangles are polyedges (A151537), but the only chordless cycles allowed are squares, e.g., this is *not* the dual graph of a Tangle: %C A333249 o-o-o %C A333249 | | %C A333249 o-o-o %C A333249 but this is: %C A333249 o-o-o %C A333249 | | | %C A333249 o-o-o %C A333249 Tangles may also be 'fixed' if we do not allow rotations and reflections (A333080) or 'free' if we allow both rotations and reflections (A333233). %H A333249 Douglas A. Torrance, <a href="https://arxiv.org/abs/1906.01541">Enumeration of planar Tangles</a>, arXiv:1906.01541 [math.CO], 2020. Sums of rows from Table 4.1 (B). %Y A333249 Cf. A151537, A333080, A333233. %K A333249 nonn,more %O A333249 0,3 %A A333249 _Douglas A. Torrance_, Mar 13 2020 %E A333249 a(11)-a(13) from _John Mason_, Feb 15 2023