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 A333233 #18 Feb 14 2023 12:55:15 %S A333233 1,1,2,5,16,55,221,947,4239,19452,90791,428839,2043548,9807941 %N A333233 Number of free Tangles of size n. %C A333233 a(n) is the number of free 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 'free', we mean that we allow rotations and reflections. %C A333233 Tangles may also be 'fixed', i.e., if we do not allow rotations and reflections (A333080). %C A333233 Tangles whose dual graphs are trees correspond exactly to diagonal polyominoes (A056841). %C A333233 Dual graphs of Tangles are polysticks (A019988), but the only chordless cycles allowed are squares, e.g., this is *not* the dual graph of a Tangle: %C A333233 o-o-o %C A333233 | | %C A333233 o-o-o %C A333233 but this is: %C A333233 o-o-o %C A333233 | | | %C A333233 o-o-o %H A333233 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 (C). %Y A333233 Cf. A019988, A056841, A333080. %K A333233 nonn,hard,more %O A333233 0,3 %A A333233 _Douglas A. Torrance_, Mar 12 2020 %E A333233 a(11)-a(13) from _John Mason_, Feb 14 2023