A211993 A list of ordered partitions of the positive integers.

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..131.

Example

A table of partitions.
--------------------------------------------
.              Expanded       Geometric
Partitions     arrangement    model
--------------------------------------------
1;             1;             |*|
--------------------------------------------
2;             . 2;           |* *|
1,1;           1,1;           |o|*|
--------------------------------------------
1,1,1;         1,1,1;         |o|o|*|
2,1;           . 2,1;         |o o|*|
3;             . . 3;         |* * *|
--------------------------------------------
4,;            . . . 4;       |* * * *|
2,2;           . 2,. 2;       |* *|* *|
3,1;           . . 3,1;       |o o o|*|
2,1,1,;        . 2,1,1;       |o o|o|*|
1,1,1,1;       1,1,1,1;       |o|o|o|*|
--------------------------------------------
1,1,1,1,1;     1,1,1,1,1;     |o|o|o|o|*|
2,1,1,1;       . 2,1,1,1;     |o o|o|o|*|
3,1,1;         . . 3,1,1;     |o o o|o|*|
2,2,1;         . 2,. 2,1;     |o o|o o|*|
4,1;           . . . 4,1;     |o o o o|*|
3,2;           . . 3,. 2;     |* * *|* *|
5;             . . . . 5;     |* * * * *|
--------------------------------------------
6;             . . . . . 6;   |* * * * * *|
3,3;           . . 3,. . 3;   |* * *|* * *|
4,2;           . . . 4,. 2;   |* * * *|* *|
2,2,2;         . 2,. 2,. 2;   |* *|* *|* *|
5,1;           . . . . 5,1;   |o o o o o|*|
3,2,1;         . . 3,. 2,1;   |o o o|o o|*|
4,1,1;         . . . 4,1,1;   |o o o o|o|*|
2,2,1,1;       . 2,. 2,1,1;   |o o|o o|o|*|
3,1,1,1;       . . 3,1,1,1;   |o o o|o|o|*|
2,1,1,1,1;     . 2,1,1,1,1;   |o o|o|o|o|*|
1,1,1,1,1,1;   1,1,1,1,1,1;   |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.

Other versions are A026792, A211992, A211994. See also A211983, A211984, A211989, A211999. Spiral arrangements are A211985-A211988, A211995-A211998.

Cf. A000041, A026905, A135010, A138121, A138137, A138879, A182703, A206437.

Sequence in context: A205565 A064531 A274468 * A185646 A037829 A270992

Adjacent sequences: A211990 A211991 A211992 * A211994 A211995 A211996

Keyword

nonn,tabf

Author

Omar E. Pol, Aug 18 2012

Status

approved