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A211993
A list of ordered partitions of the positive integers.
4
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.
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.
Sequence in context: A205565 A064531 A274468 * A185646 A037829 A270992
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Aug 18 2012
STATUS
approved