cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A354382 Number of free pseudo-polyarcs with n cells.

Original entry on oeis.org

2, 32, 700, 21943, 737164, 25959013, 938559884
Offset: 1

Views

Author

Aaron N. Siegel, May 24 2022

Keywords

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).
		

Crossrefs

A354403 Number of one-sided pseudo-polytans with n cells.

Original entry on oeis.org

1, 15, 171, 2799, 46933, 831358, 15085844, 279317154, 5247744254
Offset: 1

Views

Author

Aaron N. Siegel, May 25 2022

Keywords

Comments

As A354380, but with mirror-image figures counted as distinct.

Crossrefs

A354405 Number of fixed pseudo-polytans with n cells.

Original entry on oeis.org

4, 47, 684, 11010, 187732, 3322341, 60343376, 1117211474, 20990977016
Offset: 1

Views

Author

Aaron N. Siegel, May 25 2022

Keywords

Crossrefs

Showing 1-3 of 3 results.