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.

A211985 A list of certain compositions which arise from the ordered partitions of the positive integers in which the shells of each integer are arranged as a spiral.

Original entry on oeis.org

1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 4, 2, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 5, 2, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 4, 6, 3, 3, 4, 2, 2, 2, 2, 1, 4, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 3, 1, 5, 1, 7, 3, 4, 2, 5, 2, 2, 3, 1, 5, 1, 1, 2, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 4, 1, 1, 2, 2, 2, 1, 4, 2, 1, 3, 3, 1, 6
Offset: 1

Views

Author

Omar E. Pol, Aug 19 2012

Keywords

Comments

In order to construct this sequence we use the following rules:
- Consider the partitions of positive integers.
- For each positive integer its shells must be arranged in a spiral.
- The sequence lists one spiral for each positive integer.
- If the integer j is odd then we use the same spiral of A211995.
- If the integer j is even then the first composition listed of each spiral is j.

Examples

			--------------------------------------------
.               Expanded        Geometric
Compositions   arrangement        model
--------------------------------------------
1;                 1;             |*|
--------------------------------------------
2;                 . 2;           |* *|
1,1;               1,1;           |o|*|
--------------------------------------------
3;               3 . .;         |* * *|
1,1,1;           1,1,1;         |*|o|o|
1,2;             1,. 2;         |*|o o|
--------------------------------------------
4,;              . . . 4;       |* * * *|
2,2;             . 2,. 2;       |* *|* *|
1,2,1;           1,. 2,1;       |o|o o|*|
1,1,1,1,;        1,1,1,1;       |o|o|o|*|
3,1;             3 . .,1;       |o o o|*|
--------------------------------------------
5;             5 . . . .;     |* * * * *|
2,3;           2 .,3 . .;     |* *|* * *|
1,3,1;         1,3 . .,1;     |*|o o o|o|
1,1,1,1,1;     1,1,1,1,1;     |*|o|o|o|o|
1,1,2,1;       1,1,. 2,1;     |*|o|o o|o|
1,2,2;         1,. 2,. 2;     |*|o o|o o|
1,4;           1,. . . 4;     |*|o o o o|
--------------------------------------------
6;             . . . . . 6;   |* * * * * *|
3,3;           . . 3,. . 3;   |* * *|* * *|
4,2;           . . . 4,. 2;   |* * * *|* *|
2,2,2;         . 2,. 2,. 2;   |* *|* *|* *|
1,4,1;         1,. . . 4,1;   |o|o o o o|*|
1,2,2,1;       1,. 2,. 2,1;   |o|o o|o o|*|
1,1,2,1,1;     1,1,. 2,1,1;   |o|o|o o|o|*|
1,1,1,1,1,1;   1,1,1,1,1,1;   |o|o|o|o|o|*|
1,3,1,1;       1,3 . .,1,1;   |o|o o o|o|*|
2,3,1;         2 .,3 . .,1;   |o o|o o o|*|
5,1;           5 . . . .,1;   |o o o o o|*|
--------------------------------------------
Note that * is a unitary element of every part of the last section of j.

Crossrefs

Rows sums give A036042, n>=1.
Mirror of A211986. Other spiral versions are A211987, A211988, A211995-A211998. See also A026792, A211983, A211984, A211989, A211992, A211993, A211994, A211999.
Cf. A000041, A026905, A135010, A138121, A138137, A138879, A182703, A206437.

A211994 A list of ordered partitions of the positive integers.

Original entry on oeis.org

1, 1, 1, 2, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 2, 2, 4, 5, 3, 2, 4, 1, 2, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 1, 1, 3, 2, 1, 5, 1, 2, 2, 2, 4, 2, 3, 3, 6, 7, 4, 3, 5, 2, 3, 2, 2, 6, 1, 3, 3, 1, 4, 2, 1, 2, 2, 2, 1, 5, 1, 1, 3, 2, 1, 1, 4, 1, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

Omar E. Pol, Aug 18 2012

Keywords

Comments

The order of the partitions of the odd integers is the same as A026792. The order of the partitions of the even integers is the same as A211992.

Examples

			A table of partitions.
--------------------------------------------
.              Expanded       Geometric
Partitions     arrangement    model
--------------------------------------------
1;             1;             |*|
--------------------------------------------
1,1;           1,1;           |o|*|
2;             . 2;           |* *|
--------------------------------------------
3;             . . 3;         |* * *|
2,1;           . 2,1;         |o o|*|
1,1,1;         1,1,1;         |o|o|*|
--------------------------------------------
1,1,1,1;       1,1,1,1;       |o|o|o|*|
2,1,1;         . 2,1,1;       |o o|o|*|
3,1;           . . 3,1;       |o o o|*|
2,2;           . 2,. 2;       |* *|* *|
4;             . . . 4;       |* * * *|
--------------------------------------------
5;             . . . . 5;     |* * * * *|
3,2;           . . 3,. 2;     |* * *|* *|
4,1;           . . . 4,1;     |o o o o|*|
2,2,1;         . 2,. 2,1;     |o o|o o|*|
3,1,1;         . . 3,1,1;     |o o o|o|*|
2,1,1,1;       . 2,1,1,1;     |o o|o|o|*|
1,1,1,1,1;     1,1,1,1,1;     |o|o|o|o|*|
--------------------------------------------
1,1,1,1,1,1;   1,1,1,1,1,1;   |o|o|o|o|o|*|
2,1,1,1,1;     . 2,1,1,1,1;   |o o|o|o|o|*|
3,1,1,1;       . . 3,1,1,1;   |o o o|o|o|*|
2,2,1,1;       . 2,. 2,1,1;   |o o|o o|o|*|
4,1,1;         . . . 4,1,1;   |o o o o|o|*|
3,2,1;         . . 3,. 2,1;   |o o o|o o|*|
5,1;           . . . . 5,1;   |o o o o o|*|
2,2,2;         . 2,. 2,. 2;   |* *|* *|* *|
4,2;           . . . 4,. 2;   |* * * *|* *|
3,3;           . . 3,. . 3;   |* * *|* * *|
6;             . . . . . 6;   |* * * * * *|
--------------------------------------------
Note that * is a unitary element of every part of the last section of j.

Crossrefs

Rows sums give A036042, n>=1.
Other versions are A026792, A211992, A211993. See also A211983, A211984, A211989, A211999. Spiral arrangements are A211985-A211988, A211995-A211998.
Cf. A000041, A026905, A135010, A138121, A138137, A138879, A182703, A206437.

A211986 A list of certain compositions which arise from the ordered partitions of the positive integers in which the shells of each integer are arranged as the arms of a spiral.

Original entry on oeis.org

1, 2, 1, 1, 3, 1, 1, 1, 2, 1, 4, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 3, 5, 3, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 4, 1, 6, 3, 3, 2, 4, 2, 2, 2, 1, 4, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 2, 1, 5, 7, 4, 3, 5, 2, 3, 2, 2, 1, 5, 1, 1, 3, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 4, 1, 1, 2, 2, 2, 1, 2, 4, 1, 3, 3, 1, 6, 1
Offset: 1

Views

Author

Omar E. Pol, Aug 19 2012

Keywords

Comments

In order to construct this sequence we use the following rules:
- Consider the partitions of positive integers.
- For each positive integer its shells must be arranged as the arms of a spiral.
- The sequence lists one spiral for each positive integer.
- If the integer j is odd then the first composition listed of each spiral is j.
- If the integer j is even then we use the same spiral of A211988.

Examples

			----------------------------------------------
.                 Expanded         Geometric
Compositions     arrangement         model
----------------------------------------------
1;                    1;              |*|
----------------------------------------------
2;                  2 .;            |* *|
1,1;                1,1;            |*|o|
----------------------------------------------
3;                  . . 3;          |* * *|
1,1,1;              1,1,1;          |o|o|*|
2,1;                2 .,1;          |o o|*|
----------------------------------------------
4,;               4 . . .;        |* * * *|
2,2;              2 .,2 .;        |* *|* *|
1,2,1;            1,2 .,1;        |*|o o|o|
1,1,1,1,;         1,1,1,1;        |*|o|o|o|
1,3;              1,. . 3;        |*|o o o|
----------------------------------------------
5;                . . . . 5;      |* * * * *|
3,2;              . . 3,. 2;      |* * *|* *|
1,3,1;            1,. . 3,1;      |o|o o o|*|
1,1,1,1,1;        1,1,1,1,1;      |o|o|o|o|*|
1,2,1,1;          1,2 .,1,1;      |o|o o|o|*|
2,2,1;            2 .,2 .,1;      |o o|o o|*|
4,1;              4 . . .,1;      |o o o o|*|
----------------------------------------------
6;              6 . . . . .;    |* * * * * *|
3,3;            3 . .,3 . .;    |* * *|* * *|
2,4;            2 .,4 . . .;    |* *|* * * *|
2,2,2;          2 .,2 .,2 .;    |* *|* *|* *|
1,4,1;          1,4 . . .,1;    |*|o o o o|o|
1,2,2,1;        1,2 .,2 .,1;    |*|o o|o o|o|
1,1,2,1,1;      1,1,2 .,1,1;    |*|o|o o|o|o|
1,1,1,1,1,1;    1,1,1,1,1,1;    |*|o|o|o|o|o|
1,1,3,1;        1,1,. . 3,1;    |*|o|o o o|o|
1,3,2;          1,. . 3,. 2;    |*|o o o|o o|
1,5;            1,. . . . 5;    |*|o o o o o|
------------------------------------------------
Note that * is a unitary element of every part of the last section of j.

Links

Crossrefs

Rows sums give A036042, n>=1.
Mirror of A211985. Other spiral versions are A211987, A211988, A211995-A211998. See also A026792, A211983, A211984, A211989, A211992, A211993, A211994, A211999.
Cf. A000041, A026905, A135010, A138121, A138137, A138879, A182703, A206437.

A211987 A list of certain compositions which arise from the ordered partitions of the positive integers in which the shells of each integer are arranged as a spiral.

Original entry on oeis.org

1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 4, 2, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 4, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 3, 5, 6, 3, 3, 4, 2, 2, 2, 2, 1, 4, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 3, 1, 5, 1, 1, 6, 1, 3, 3, 1, 4, 2, 1
Offset: 1

Views

Author

Omar E. Pol, Aug 18 2012

Keywords

Comments

In order to construct this sequence we use the following rules:
- Consider the partitions of positive integers.
- For each positive integer its shells must be arranged in a spiral.
- The sequence lists one spiral for each positive integer.
- If the integer j is odd then the last composition listed of each spiral is j.
- If the integer j is even then the first composition listed of each spiral is j.
This sequence represents a three-dimensional structure in which each column contains parts of the same size.

Examples

			----------------------------------------------
.                Expanded        Geometric
Compositions    arrangement        model
----------------------------------------------
1;                  1;              |*|
----------------------------------------------
2;                  . 2;            |* *|
1,1;                1,1;            |o|*|
----------------------------------------------
1,2;              1,. 2;          |*|o o|
1,1,1;            1,1,1;          |*|o|o|
3;                3 . .;          |* * *|
----------------------------------------------
4,;               . . . 4;        |* * * *|
2,2;              . 2,. 2;        |* *|* *|
1,2,1;            1,. 2,1;        |o|o o|*|
1,1,1,1,;         1,1,1,1;        |o|o|o|*|
3,1;              3 . .,1;        |o o o|*|
----------------------------------------------
1,4;            1,. . . 4;      |*|o o o o|
1,2,2;          1,. 2,. 2;      |*|o o|o o|
1,1,2,1;        1,1,. 2,1;      |*|o|o o|o|
1,1,1,1,1;      1,1,1,1,1;      |*|o|o|o|o|
1,3,1;          1,3 . .,1;      |*|o o o|o|
2,3;            2 .,3 . .;      |* *|* * *|
5;              5 . . . .;      |* * * * *|
----------------------------------------------
6;              . . . . . 6;    |* * * * * *|
3,3;            . . 3,. . 3;    |* * *|* * *|
4,2;            . . . 4,. 2;    |* * * *|* *|
2,2,2;          . 2,. 2,. 2;    |* *|* *|* *|
1,4,1;          1,. . . 4,1;    |o|o o o o|*|
1,2,2,1;        1,. 2,. 2,1;    |o|o o|o o|*|
1,1,2,1,1;      1,1,. 2,1,1;    |o|o|o o|o|*|
1,1,1,1,1,1;    1,1,1,1,1,1;    |o|o|o|o|o|*|
1,3,1,1;        1,3 . .,1,1;    |o|o o o|o|*|
2,3,1;          2 .,3 . .,1;    |o o|o o o|*|
5,1;            5 . . . .,1;    |o o o o o|*|
----------------------------------------------
Note that * is a unitary element of every part of the last section of j.

Links

Crossrefs

Rows sums give A036042, n>=1.
Mirror of A211988. Other spiral versions are A211985, A211986, A211995-A211998. See also A026792, A211983, A211984, A211989, A211992, A211993, A211994, A211999.
Cf. A000041, A026905, A135010, A138121, A138137, A138879, A182703, A206437.
Showing 1-4 of 4 results.

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