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
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