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A333249
Number of one-sided Tangles of size n.
1
1, 1, 2, 7, 25, 99, 415, 1849, 8368, 38712, 181111, 856833, 4085025, 19612082
OFFSET
0,3
COMMENTS
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.
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:
o-o-o
| |
o-o-o
but this is:
o-o-o
| | |
o-o-o
Tangles may also be 'fixed' if we do not allow rotations and reflections (A333080) or 'free' if we allow both rotations and reflections (A333233).
LINKS
Douglas A. Torrance, Enumeration of planar Tangles, arXiv:1906.01541 [math.CO], 2020. Sums of rows from Table 4.1 (B).
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Douglas A. Torrance, Mar 13 2020
EXTENSIONS
a(11)-a(13) from John Mason, Feb 15 2023
STATUS
approved