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 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.
LINKS
EXAMPLE
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. Expanded Geometric
Compositions arrangement model
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1; 1; |*|
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2; . 2; |* *|
1,1; 1,1; |o|*|
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1,2; 1,. 2; |*|o o|
1,1,1; 1,1,1; |*|o|o|
3; 3 . .; |* * *|
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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|*|
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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 . . . .; |* * * * *|
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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|*|
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Note that * is a unitary element of every part of the last section of j.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Aug 18 2012
STATUS
approved