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A354382
Number of free pseudo-polyarcs with n cells.
3
2, 32, 700, 21943, 737164, 25959013, 938559884
OFFSET
1,1
COMMENTS
See A057787 for a description of polyarcs. The pseudo-polyarcs are constructed in the same way as ordinary polyarcs, but allowing for corner-connections. Thus they generalize polyarcs in the same way that pseudo-polyominoes (aka polyplets, A030222) generalize ordinary polyominoes (A000105). They can also be viewed as the "rounded" variant of pseudo-polytans (A354380), in the same way that ordinary polyarcs are the rounded variant of ordinary polytans (A006074).
Two figures are considered equivalent if they differ only by a rotation or reflection.
The pseudo-polyarcs grow tremendously fast, much faster than most polyforms. The initial data that have been computed suggest an asymptotic growth rate of at least 36^n.
LINKS
Aaron N. Siegel, Illustration showing a(2) = 32. The color of each figure corresponds to its number of symmetries.
EXAMPLE
a(10) = 32, because there are 32 ways of adjoining two monarcs: 7 distinct edge-to-edge joins, and 25 distinct corner-to-corner joins (including one double-corner join involving two concave arcs).
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Aaron N. Siegel, May 24 2022
STATUS
approved