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A211983
A list of ordered partitions of the positive integers in which the shells of each integer are assembled by their tails.
8
1, 2, 1, 1, 2, 1, 1, 1, 1, 3, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 3, 1, 4, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 2, 5, 6, 3, 3, 4, 2, 2, 2, 2, 4, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 2, 1, 5, 1, 6, 1, 3, 3, 1, 4, 2, 1, 2, 2, 2, 1, 4, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 2, 1, 1, 5, 1, 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 A211999. The order of the partitions of the even integers is the same as A211989.
EXAMPLE
A table of partitions.
--------------------------------------------
. Expanded Geometric
Partitions arrangement model
--------------------------------------------
1; 1; |*|
--------------------------------------------
2; . 2; |* *|
1,1; 1,1; |o|*|
--------------------------------------------
2,1; . 2,1; |o o|*|
1,1,1; 1,1,1; |o|o|*|
3; . . 3; |* * *|
--------------------------------------------
4; . . . 4; |* * * *|
2,2; . 2,. 2; |* *|* *|
2,1,1; . 2,1,1; |o o|o|*|
1,1,1,1; 1,1,1,1; |o|o|o|*|
3,1; . . 3,1; |o o o|*|
--------------------------------------------
4,1; . . . 4,1; |o o o o|*|
2,2,1; . 2,. 2,1; |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|*|
3,1,1; . . 3,1,1; |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; |* *|* *|* *|
4,1,1; . . . 4,1,1; |o o o o|o|*|
2,2,1,1; . 2,. 2,1,1; |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|*|
3,1,1,1; . . 3,1,1,1; |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|*|
--------------------------------------------
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 A211984, A211989, A211999. See also A026792, A211992-A211994. Spiral arrangements are A211985-A211988, A211995-A211998.
Sequence in context: A352999 A280747 A110955 * A173264 A056731 A042974
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Aug 19 2012
STATUS
approved