A354382 Number of free pseudo-polyarcs with n cells.

2, 32, 700, 21943, 737164, 25959013, 938559884

Offset: 1

Author

Aaron N. Siegel, May 24 2022

Keywords

• nonn
• hard
• more

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.

Examples

			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).
		

Links

• Aaron N. Siegel, Illustration showing a(2) = 32. The color of each figure corresponds to its number of symmetries.

Crossrefs

Cf. A057787, A354380, A006074, A000105, A030222.