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 A333080 #26 Feb 19 2023 12:13:26 %S A333080 1,2,6,22,88,372,1626,7292,33309,154374,723740,3425124,16336747, %T A333080 78437858 %N A333080 Number of fixed Tangles of size n. %C A333080 a(n) is the number of fixed 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 'fixed', we mean that we do not allow rotations or reflections. %C A333080 Dual graphs of Tangles are polyedges (A096267), but the only chordless cycles allowed are squares, e.g., this is *not* the dual graph of a Tangle: %C A333080 o-o-o %C A333080 | | %C A333080 o-o-o %C A333080 but this is: %C A333080 o-o-o %C A333080 | | | %C A333080 o-o-o %H A333080 Douglas A. Torrance, <a href="https://arxiv.org/abs/1906.01541">Enumeration of planar Tangles</a>, arXiv:1906.01541 [math.CO], 2019-2020. Sums of rows from Table 4.1 (A). %Y A333080 Dual graphs of Tangles which are trees are bond trees on the square lattice (A308409), free Tangles (A333233). %K A333080 nonn,hard,more %O A333080 0,2 %A A333080 _Douglas A. Torrance_, Mar 07 2020 %E A333080 a(11)-a(13) from _John Mason_, Feb 14 2023