OFFSET
1,2
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.
LINKS
EXAMPLE
----------------------------------------------
. 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.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Aug 19 2012
STATUS
approved