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A230440
Triangle read by rows in which row n lists A000041(n-1) 1's followed by the list of partitions of n that do not contain 1 as a part in colexicographic order.
3
1, 1, 2, 1, 1, 3, 1, 1, 1, 2, 2, 4, 1, 1, 1, 1, 1, 3, 2, 5, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 4, 2, 3, 3, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 5, 2, 4, 3, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 2, 2, 3, 3, 2, 6, 2, 5, 3, 4, 4, 8
OFFSET
1,3
COMMENTS
The n-th row of triangle lists the parts of the n-th section of the set of partitions of any integer >= n. For the definition of "section" see A135010.
EXAMPLE
Illustration of initial terms (row = 1..6). The table shows the six sections of the set of partitions of 6 in three ways. Note that before the dissection, the set of partitions was in colexicographic order, see A211992. More generally, in a master model, the six sections of the set of partitions of 6 also can be interpreted as the first six sections of the set of partitions of any integer >= 6.
---------------------------------------------------------
n j Diagram Parts Parts
---------------------------------------------------------
. _
1 1 |_| 1; 1;
. _
2 1 _| | 1, 1,
2 2 |_ _| 2; 2;
. _
3 1 | | 1, 1,
3 2 _ _| | 1, 1,
3 3 |_ _ _| 3; 3;
. _
4 1 | | 1, 1,
4 2 | | 1, 1,
4 3 _ _ _| | 1, 1,
4 4 |_ _| | 2,2, 2,2,
4 5 |_ _ _ _| 4; 4;
. _
5 1 | | 1, 1,
5 2 | | 1, 1,
5 3 | | 1, 1,
5 4 | | 1, 1,
5 5 _ _ _ _| | 1, 1,
5 6 |_ _ _| | 3,2, 3,2,
5 7 |_ _ _ _ _| 5; 5;
. _
6 1 | | 1, 1,
6 2 | | 1, 1,
6 3 | | 1, 1,
6 4 | | 1, 1,
6 5 | | 1, 1,
6 6 | | 1, 1,
6 7 _ _ _ _ _| | 1, 1,
6 8 |_ _| | | 2,2,2, 2,2,2,
6 9 |_ _ _ _| | 4,2, 4,2,
6 10 |_ _ _| | 3,3, 3,3,
6 11 |_ _ _ _ _ _| 6; 6;
...
Triangle begins:
[1];
[1],[2];
[1],[1],[3];
[1],[1],[1],[2,2],[4];
[1],[1],[1],[1],[1],[3,2],[5];
[1],[1],[1],[1],[1],[1],[1],[2,2,2],[4,2],[3,3],[6];
...
CROSSREFS
Positive terms of A228716.
Row n has length A138137(n).
Row sums give A138879.
Right border gives A000027.
Sequence in context: A207377 A135010 A138138 * A283495 A196931 A175465
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Oct 18 2013
STATUS
approved