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.

A369364 Number of free n-celled (planar) polyhexes with the least number (A369363(n)) of inequivalent cells.

Original entry on oeis.org

1, 1, 1, 5, 1, 1, 1, 7, 3, 9, 9, 4, 2, 27, 10, 4
Offset: 1

Views

Author

Pontus von Brömssen, Jan 22 2024

Keywords

Links

Crossrefs

Cf. A000228, A367759, A369363, A369367.

Extensions

a(13)-a(16) from John Mason, Sep 24 2024

A367758 Least number of inequivalent cells in a polyomino with n cells.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 2, 4, 4, 5, 3, 4, 5, 6, 3, 5, 6, 7, 4, 5, 7, 8, 4, 6, 8, 9, 5, 6, 9, 10, 5, 7, 10, 11, 6, 7, 11, 12, 6, 8, 12, 13, 7, 8, 13, 14, 7, 9, 14, 15, 8, 9, 15, 16, 8, 10, 16, 17, 9, 10, 17, 18, 9, 11, 18, 19, 10, 11, 19, 20, 10, 12, 20, 21, 11, 12, 21, 22, 11, 13, 22, 23
Offset: 1

Views

Author

Pontus von Brömssen, Nov 29 2023

Keywords

Comments

Two cells in a polyomino are equivalent if there is a symmetry of the polyomino that takes one of the cells to the other.
Equivalently, a(n) is the least number of pointed polyominoes (A126202) corresponding to a given polyomino with n cells.

Examples

			The X pentomino has 2 inequivalent cells and no pentomino have all cells equivalent, so a(5) = 2.

Links

Crossrefs

Cf. A126202, A255890, A367759, A369363, A369366, A376798.

Formula

a(n) > n/8.
From John Mason and Pontus von Brömssen, Oct 08 2024: (Start)
For n != 1,5, n = 8*k + c, for integers k and c, k >= 0, 0 <= c <= 7:
if c = 0 or 1 then a(n) = k + c + 1;
if c = 2 or 6 then a(n) = 2*k + (c+2)/4;
if c = 3 or 7 then a(n) = 2*k + (c+5)/4;
if c = 4 then a(n) = k + 1;
if c = 5 then a(n) = k + 3.
a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-8) - a(n-9) + a(n-10) - a(n-11) for n >= 17.
a(n) = 2*a(n-8) - a(n-16) for n >= 22. (End)

Extensions

a(14)-a(18) from John Mason, Sep 19 2024
More terms from John Mason, Oct 08 2024

A369366 Least number of inequivalent cells in a polyiamond with n cells.

Original entry on oeis.org

1, 1, 2, 2, 3, 1, 3, 3, 3, 3, 6, 2, 4, 4, 4, 4, 9, 2
Offset: 1

Views

Author

Pontus von Brömssen, Jan 22 2024

Keywords

Comments

Equivalently, a(n) is the least number of free rooted (or pointed) polyiamonds (A369365) corresponding to a given polyiamond with n cells.

Links

Crossrefs

Cf. A000577, A367758, A369363, A369365, A369367.

Extensions

a(18) from John Mason, Sep 20 2024

A373636 Number of free n-celled (planar) polyhexes to which two inequivalent cells can be adjoined such that the two resulting free (n+1)-celled polyhexes are identical.

Original entry on oeis.org

0, 0, 0, 1, 1, 0, 7, 8, 0, 40
Offset: 1

Views

Author

Pontus von Brömssen, Jun 13 2024

Keywords

Comments

Two cells that can be adjoined to an n-celled polyhex are equivalent if there is an isomorphism between the two resulting (n+1)-celled polyhexes that maps the adjoined cell of the first to the adjoined cell of the second.

Links

Crossrefs

Cf. A369363, A373635, A373637.

A369362 Number of free rooted (or pointed) (planar) polyhexes with n cells.

Original entry on oeis.org

1, 1, 5, 18, 87, 422, 2176, 11200, 58231, 302597, 1574055, 8184032, 42544369, 221083979, 1148571336, 1670519061
Offset: 1

Views

Author

Pontus von Brömssen, Jan 22 2024

Keywords

Links

Crossrefs

Cf. A000228, A126202, A369363, A369365.

Extensions

a(13)-a(16) from John Mason, Sep 24 2024
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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