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 1-4 of 4 results.

A367438 Number of polyominoes with n cells that have the maximum degree (A367437(n)) in the polyomino graph PG(n) defined in A367435.

Original entry on oeis.org

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

Views

Author

Pontus von Brömssen, Nov 18 2023

Keywords

Links

Crossrefs

Cf. A367125, A367435, A367437.

A367124 Maximum degree of the n-omino graph defined in A098891.

Original entry on oeis.org

0, 0, 1, 4, 10, 28, 39, 68, 81, 116, 140, 186, 204
Offset: 1

Views

Author

Pontus von Brömssen, Nov 05 2023

Keywords

Comments

Largest number of free polyominoes that can be made from a polyomino with n cells by moving one of its cells (not counting itself).

Examples

			For 1 <= n <= 12, the following polyominoes have the maximum degree in the polyomino graph of their respective sizes (see also link):
                                                _             _
             _           _        _    _      _| |     _     | |
        _   | |   _     | |     _| |  | |_   |_  |   _| |    | |_
   _   | |  | |  | |_   | |_   |_  |  |   |    | |  |_  |_   |   |
  |_|  |_|  |_|  |_ _|  |_ _|    |_|  |_ _|    |_|    |_ _|  |_ _|
                     _          _      _        _
     _      _       | |       _| |    | |      | |_      _ _
   _| |    | |      | |      |_  |_   | |_ _   |   |_   |   |_ _
  |_  |_   | |_ _   | |_ _     |   |  |  _  |  |  _  |  |  _ _  |
    |   |  |     |  |     |    |   |  | |_| |  | |_| |  | |_ _| |
    |_ _|  |_ _ _|  |_ _ _|    |_ _|  |_ _ _|  |_ _ _|  |_ _ _ _|

Links

Crossrefs

Cf. A098891, A367123, A367125, A367437.
Row maxima of A367126.

Formula

a(n) >= A367437(n).

A367435 Let PG(n) be the graph with one node for each free n-celled polyomino and edges between nodes corresponding to polyominoes that can be obtained from each other by moving one cell, where the intermediate (the set of cells remaining when the cell to be moved is detached) is required to be a (connected) polyomino. a(n) is the number of edges in PG(n).

Original entry on oeis.org

0, 0, 1, 8, 45, 254, 1258, 6181, 28062, 125714, 550402, 2394654, 10326665
Offset: 1

Views

Author

Pontus von Brömssen, Nov 18 2023

Keywords

Comments

Equivalently, there is an edge between two nodes if the corresponding n-celled polyominoes can be obtained from the same (n-1)-celled polyomino by adding one cell.
In the n-omino graph defined in A098891, the intermediate is not required to be a polyomino, so PG(n) is a spanning subgraph of that graph. For n = 5, for example, there is an edge between the V and W pentominoes in the graph in A098891, but not in PG(5).

Links

Crossrefs

Half the row sums of A367439.
Cf. A000105, A098891, A367436, A367437, A367438, A367440, A367441, A367443.

Formula

a(n) <= A098891(n).

A367439 a(n) is the degree of the polyomino with binary code A246521(n+1) in the polyomino graph PG(n) defined in A367435.

Original entry on oeis.org

0, 0, 1, 1, 4, 3, 4, 3, 2, 10, 8, 3, 9, 10, 9, 8, 9, 10, 8, 4, 2, 15, 28, 15, 12, 12, 10, 17, 14, 19, 20, 15, 14, 15, 13, 18, 20, 9, 14, 13, 17, 4, 12, 16, 18, 11, 9, 10, 15, 22, 19, 10, 19, 14, 16, 3, 36, 36, 35, 31, 28, 30, 36, 22, 29, 37, 16, 11, 28, 13, 24
Offset: 1

Views

Author

Pontus von Brömssen, Nov 18 2023

Keywords

Comments

Number of free polyominoes that can be made from the polyomino with binary code A246521(n+1) by moving one of its cells (not counting itself), where the intermediate (the set of cells remaining when the cell to be moved is detached) is required to be a (connected) polyomino.
Can be read as an irregular triangle, whose m-th row contains A000105(m) terms, m >= 1.

Examples

			As an irregular triangle:
   0;
   0;
   1, 1;
   4, 3, 4, 3,  2;
  10, 8, 3, 9, 10, 9, 8, 9, 10, 8, 4, 2;
  ...
For n = 8, A246521(8+1) = 30 is the binary code of the S-tetromino. By moving one cell of the S-tetromino, we can obtain the L, O, and T tetrominoes (but not the I tetromino), so a(8) = 3.

Links

Crossrefs

Cf. A000105, A246521, A367126, A367435, A367437 (row maxima), A367438, A367443.

Formula

a(n) <= A367126(n).
Showing 1-4 of 4 results.

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