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A228531 Triangle read by rows in which row n lists the partitions of n in reverse lexicographic order. 3
1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 4, 2, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 5, 2, 3, 1, 4, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 6, 3, 3, 2, 4, 2, 2, 2, 1, 5, 1, 2, 3, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 7, 3, 4, 2, 5, 2, 2, 3, 1, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The representation of the partitions (for fixed n) is as (weakly) increasing lists of parts, the order between individual partitions (for the same n) is (list-)reversed lexicographic; see examples. [Joerg Arndt, Sep 03 2013]

Also compositions in the triangle of A066099 that are in nondecreasing order.

The equivalent sequence for compositions (ordered partitions) is A066099.

Row n has length A006128(n).

Row sums give A066186.

LINKS

Table of n, a(n) for n=1..87.

EXAMPLE

Illustration of initial terms:

---------------------------------

.                    Ordered

n  j     Diagram     partition

---------------------------------

.              _

1  1          |_|    1;

.            _ _

2  1        |  _|    2,

2  2        |_|_|    1, 1;

.          _ _ _

3  1      |  _ _|    3,

3  2      | |  _|    1, 2,

3  3      |_|_|_|    1, 1, 1;

.        _ _ _ _

4  1    |    _ _|    4,

4  2    |  _|_ _|    2, 2,

4  3    | |  _ _|    1, 3,

4  4    | | |  _|    1, 1, 2,

4  5    |_|_|_|_|    1, 1, 1, 1;

.

Triangle begins:

[1];

[2],[1,1];

[3],[1,2],[1,1,1];

[4],[2,2],[1,3],[1,1,2],[1,1,1,1];

[5],[2,3],[1,4],[1,2,2],[1,1,3],[1,1,1,2],[1,1,1,1,1];

[6],[3,3],[2,4],[2,2,2],[1,5],[1,2,3],[1,1,4],[1,1,2,2],[1,1,1,3],[1,1,1,1,2],[1,1,1,1,1,1];

[7],[3,4],[2,5],[2,2,3],[1,6],[1,3,3],[1,2,4],[1,2,2,2],[1,1,5],[1,1,2,3],[1,1,1,4],[1,1,1,2,2],[1,1,1,1,3],[1,1,1,1,1,2],[1,1,1,1,1,1,1];

...

CROSSREFS

Cf. A000041, A066099, A026791, A026792, A211992, A228351.

Sequence in context: A057898 A094293 A036036 * A244316 A076259 A260533

Adjacent sequences:  A228528 A228529 A228530 * A228532 A228533 A228534

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Aug 30 2013

STATUS

approved

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Last modified June 18 14:52 EDT 2019. Contains 324213 sequences. (Running on oeis4.)