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.

A075679 Number of free (rotations and reflections count as same shape) polyominoids (shapes made of faces of cubes) with n squares.

Original entry on oeis.org

1, 2, 9, 54, 448, 4650, 53611, 655033, 8259635, 106371085, 1391032357, 18412269694
Offset: 1

Views

Author

Joseph Myers, Sep 24 2002

Keywords

Links

Crossrefs

Cf. A075678, A056846.
18th row of A366766.

A365995 Number of free polyominoids with n cells, allowing flat corner-connections and right-angled edge-connections.

Original entry on oeis.org

1, 2, 9, 66, 691, 9216, 134325
Offset: 1

Views

Author

Pontus von Brömssen, Sep 26 2023

Keywords

Comments

This sequence and the related sequences A365650-A365655 and A365996-A366010 count polyominoids (A075679) with different rules for how the cells can be connected. In these sequences, connections other than the specified ones are permitted, but the polyominoids must be connected through the specified connections only. The polyominoids counted by this sequence, for example, are allowed to have right-angled corner-connections and flat edge-connections, as long as they are not needed for the polyominoid to be connected. A connection is flat if the two neighboring cells lie in the same plane, otherwise it is right-angled.

Links

Crossrefs

Cf. A365996 (fixed).
21st row of A366766.
The following table lists counting sequences for free, fixed, and one-sided polyominoids with different sets of allowed connections. "|" means flat connections and "L" means right-angled connections.
corner-connections | edge-connections | free | fixed | 1-sided
-------------------+------------------+---------+---------+--------
none | | | A000105 |3*A001168| A000105
none | L | A365654 | A365655 |
none | |L | A075679 | A075678 | A056846
| | none | A000105 |3*A001168| A000105
| | | | A030222 |3*A006770| A030222
| | L | A365995 | A365996 |
| | |L | A365997 | A365998 |
L | none | A365999 | A366000 |
L | | | A366001 | A366002 |
L | L | A366003 | A366004 |
L | |L | A366005 | A366006 |
|L | none | A365652 | A365653 |
|L | | | A366007 | A366008 |
|L | L | A366009 | A366010 |
|L | |L | A365650 | A365651 |

Extensions

a(7) from Pontus von Brömssen, Mar 03 2025

A075678 Number of fixed (orientation matters) polyominoids (shapes made of faces of cubes) with n squares.

Original entry on oeis.org

3, 18, 158, 1611, 17811, 207395, 2505858, 31125711, 394982973, 5098498323, 66733261455, 883602795509, 11814191512434, 159283419280014, 2163058572006613
Offset: 1

Views

Author

Joseph Myers, Sep 24 2002

Keywords

Links

Crossrefs

Cf. A075679 (free), A056846.
18th row of A366767.

Extensions

a(13)-a(15) from John Mason, Mia Muessig, and Érika Roldán, Jul 04 2025
Showing 1-3 of 3 results.

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

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