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A026792 List of juxtaposed reverse-lexicographically ordered partitions of the positive integers. 23
1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 2, 2, 3, 1, 2, 1, 1, 1, 1, 1, 1, 5, 3, 2, 4, 1, 2, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 6, 3, 3, 4, 2, 2, 2, 2, 5, 1, 3, 2, 1, 4, 1, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 4, 3, 5, 2, 3, 2, 2, 6, 1, 3, 3, 1, 4, 2, 1, 2, 2, 2, 1, 5, 1, 1, 3, 2, 1, 1, 4, 1, 1, 1, 2, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Written as a triangle; row n has length A006128(n); row sums give A066186. Also written as an irregular tetrahedron in which T(n,j,k) is the k-th largest part of the j-th partition of n; the sum of column k in the slice n is A181187(n,k); right border of the slices gives A182715. - Omar E. Pol, Mar 25 2012

The equivalent sequence for compositions (ordered partitions) is A228351). - Omar E. Pol, Sep 03 2013

LINKS

Table of n, a(n) for n=1..111.

EXAMPLE

E.g. the partitions of 3 (3,2+1,1+1+1) appear as the string 3,2,1,1,1,1.

So the list begins:

1

2, 1, 1,

3, 2, 1, 1, 1, 1,

4, 2, 2, 3, 1, 2, 1, 1, 1, 1, 1, 1,

5, 3, 2, 4, 1, 2, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,

...

From Omar E. Pol, Sep 03 2013: (Start)

Illustration of initial terms:

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

n  j     Diagram     Partition

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

.         _

1  1     |_|         1;

.         _ _

2  1     |_  |       2,

2  2     |_|_|       1, 1;

.         _ _ _

3  1     |_ _  |     3,

3  2     |_  | |     2, 1,

3  3     |_|_|_|     1, 1, 1;

.         _ _ _ _

4  1     |_ _    |   4,

4  2     |_ _|_  |   2, 2,

4  3     |_ _  | |   3, 1,

4  4     |_  | | |   2, 1, 1,

4  5     |_|_|_|_|   1, 1, 1, 1;

...

(End)

CROSSREFS

Cf. A026791, A211992, A228351, A228531.

Sequence in context: A211028 A239001 A277648 * A139100 A237982 A239512

Adjacent sequences:  A026789 A026790 A026791 * A026793 A026794 A026795

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling

EXTENSIONS

Terms 81st, 83rd and 84th corrected by Omar E. Pol, Aug 16 2009

STATUS

approved

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Last modified May 19 22:56 EDT 2019. Contains 323411 sequences. (Running on oeis4.)