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 1-5 of 5 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

A353979 Number of one-sided polyarcs with n cells.

Original entry on oeis.org

2, 11, 36, 169, 702, 3411, 16372, 81798, 412696, 2112362, 10907492, 56782983, 297599786, 1568750187
Offset: 1

Views

Author

Aaron N. Siegel, May 12 2022

Keywords

Crossrefs

Cf. A057787.

A349101 Number of fixed polyarcs with n cells.

Original entry on oeis.org

8, 33, 144, 626, 2808, 13422, 65488, 326183, 1650784, 8444367, 43629968, 227105588, 1190399144, 6274864076
Offset: 1

Views

Author

Aaron N. Siegel, May 14 2022

Keywords

Crossrefs

A354406 Number of one-sided pseudo-polyarcs with n cells.

Original entry on oeis.org

2, 53, 1354, 43573, 1472916, 51907977, 1877071666
Offset: 1

Views

Author

Aaron N. Siegel, May 25 2022

Keywords

Comments

As A354382, but with mirror-image figures counted as distinct.

Crossrefs

A354407 Number of fixed pseudo-polyarcs with n cells.

Original entry on oeis.org

8, 187, 5416, 173548, 5891664, 207606612, 7508286664
Offset: 1

Views

Author

Aaron N. Siegel, May 25 2022

Keywords

Crossrefs

Showing 1-5 of 5 results.