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.

Previous Showing 11-20 of 26 results. Next

A366335 Number of fixed (4,2)-polyominoids with n cells.

Original entry on oeis.org

6, 60, 916, 16698, 336210, 7218768, 162185112, 3769221330, 89924613880
Offset: 1

Views

Author

Pontus von Brömssen, Oct 07 2023

Keywords

Comments

A (D,d)-polyominoid is a connected set of d-dimensional unit cubes with integer coordinates in D-dimensional space, where two cubes are connected if they share a (d-1)-dimensional facet. For example, (3,2)-polyominoids are normal polyominoids (A075678), (D,D)-polyominoids are D-dimensional polyominoes (A001168, A001931, A151830, ...), and (D,1)-polyominoids are polysticks in D dimensions (A096267, A365560, A365562, ...).

Links

Crossrefs

Cf. A366334 (free).
46th row of A366767.
Fixed (D,d)-polyominoids:
D\d| 1 2 3 4
---+--------------------------------
1 | A000012
2 | A096267 A001168
3 | A365560 A075678 A001931
4 | A365562 A366335 A366337 A151830

Extensions

a(7)-a(9) from John Mason, Jul 05 2025

A365651 Number of fixed n-polyominoids, allowing both corner- and edge-connections.

Original entry on oeis.org

3, 48, 1072, 27732, 781200
Offset: 1

Views

Author

Pontus von Brömssen, Sep 17 2023

Keywords

Links

Crossrefs

Cf. A001168 (polyominoes), A006770 (polyplets), A075678 (polyominoids), A365650 (free), A365653 (corner-connections only).
30th row of A366767.

A365653 Number of fixed n-polyominoids, allowing corner-connections only.

Original entry on oeis.org

3, 30, 554, 12453, 308313, 8055534
Offset: 1

Views

Author

Pontus von Brömssen, Sep 17 2023

Keywords

Links

Crossrefs

Cf. A075678 (polyominoids, edge-connections only), A365651 (corner- and edge-connections), A365652 (free).
27th row of A366767.

A366768 Array read by antidiagonals, where each row is the coordination sequence for the underlying graph of the polyominoids occurring in the corresponding row of A366766.

Original entry on oeis.org

1, 0, 1, 0, 2, 1, 0, 2, 0, 1, 0, 2, 0, 2, 1, 0, 2, 0, 2, 4, 1, 0, 2, 0, 2, 8, 6, 1, 0, 2, 0, 2, 12, 16, 0, 1, 0, 2, 0, 2, 16, 24, 0, 4, 1, 0, 2, 0, 2, 20, 32, 0, 8, 4, 1, 0, 2, 0, 2, 24, 40, 0, 12, 8, 8, 1, 0, 2, 0, 2, 28, 48, 0, 16, 12, 16, 0, 1
Offset: 1

Views

Author

Pontus von Brömssen, Oct 22 2023

Keywords

Comments

The underlying graph of a given type of polyominoids has all possible cells as nodes and edges between cells that are connected (respecting which types of connections are allowed). See A366766 for details on how the allowed connections are specified and on the ordering of the rows.

Examples

			Array begins:
  n\k| 0  1  2   3   4   5   6   7   8   9   10   11
  ---+----------------------------------------------
   1 | 1  0  0   0   0   0   0   0   0   0    0    0
   2 | 1  2  2   2   2   2   2   2   2   2    2    2
   3 | 1  0  0   0   0   0   0   0   0   0    0    0
   4 | 1  2  2   2   2   2   2   2   2   2    2    2
   5 | 1  4  8  12  16  20  24  28  32  36   40   44
   6 | 1  6 16  24  32  40  48  56  64  72   80   88
   7 | 1  0  0   0   0   0   0   0   0   0    0    0
   8 | 1  4  8  12  16  20  24  28  32  36   40   44
   9 | 1  4  8  12  16  20  24  28  32  36   40   44
  10 | 1  8 16  24  32  40  48  56  64  72   80   88
  11 | 1  0  0   0   0   0   0   0   0   0    0    0
  12 | 1  2  2   2   2   2   2   2   2   2    2    2
  13 | 1  8 30  68 126 180 286 348 510 572  798  852
  14 | 1 10 46 106 190 298 430 586 766 970 1198 1450
  15 | 1  0  0   0   0   0   0   0   0   0    0    0
  16 | 1  4  8  12  16  20  24  28  32  36   40   44
  17 | 1  8 30  68 126 180 286 348 510 572  798  852
  18 | 1 12 50 110 194 302 434 590 770 974 1202 1454

Links

Crossrefs

Cf. A366766, A366767.

A365998 Number of fixed polyominoids with n cells, allowing flat corner-connections and any edge-connections.

Original entry on oeis.org

3, 24, 296, 4248, 66768, 1113395
Offset: 1

Views

Author

Pontus von Brömssen, Sep 26 2023

Keywords

Links

Crossrefs

See A365995 for further details and a table of related sequences.
Cf. A365997 (free).
22nd row of A366767.

A366000 Number of fixed polyominoids with n cells, allowing right-angled corner-connections.

Original entry on oeis.org

3, 24, 344, 6024, 117756, 2453722
Offset: 1

Views

Author

Pontus von Brömssen, Sep 26 2023

Keywords

Links

Crossrefs

See A365995 for further details and a table of related sequences.
Cf. A365999 (free).
23rd row of A366767.

A366002 Number of fixed polyominoids with n cells, allowing right-angled corner-connections and flat edge-connections.

Original entry on oeis.org

3, 30, 506, 10221, 226845, 5325630
Offset: 1

Views

Author

Pontus von Brömssen, Sep 26 2023

Keywords

Links

Crossrefs

See A365995 for further details and a table of related sequences.
Cf. A366001 (free).
24th row of A366767.

A366004 Number of fixed polyominoids with n cells, allowing right-angled corner-connections and right-angled edge-connections.

Original entry on oeis.org

3, 36, 700, 15426, 368154
Offset: 1

Views

Author

Pontus von Brömssen, Sep 28 2023

Keywords

Comments

See A365995 for further details and a table of related sequences.

Links

Crossrefs

Cf. A365995, A366003 (free).
25th row of A366767.

A366006 Number of fixed polyominoids with n cells, allowing right-angled corner-connections and any edge-connections.

Original entry on oeis.org

3, 42, 838, 19323, 484371
Offset: 1

Views

Author

Pontus von Brömssen, Sep 28 2023

Keywords

Comments

See A365995 for further details and a table of related sequences.

Links

Crossrefs

Cf. A365995, A366005 (free).
26th row of A366767.

A366008 Number of fixed polyominoids with n cells, allowing any corner-connections and flat edge-connections.

Original entry on oeis.org

3, 36, 740, 17946, 475194
Offset: 1

Views

Author

Pontus von Brömssen, Sep 28 2023

Keywords

Comments

See A365995 for further details and a table of related sequences.

Links

Crossrefs

Cf. A365995, A366007 (free).
28th row of A366767.
Previous Showing 11-20 of 26 results. Next

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

Content is available under The OEIS End-User License Agreement.