|
|
A238860
|
|
Partitions with superdiagonal growth: number of partitions (p0, p1, p2, ...) of n with pi - p0 >= i.
|
|
9
|
|
|
1, 1, 1, 2, 2, 3, 4, 6, 6, 9, 11, 15, 18, 23, 26, 35, 43, 53, 64, 79, 91, 113, 135, 166, 197, 237, 277, 331, 387, 459, 541, 646, 754, 888, 1032, 1204, 1395, 1626, 1882, 2196, 2542, 2952, 3404, 3934, 4507, 5182, 5935, 6812, 7800, 8947, 10225, 11709, 13354, 15231, 17314, 19685, 22316, 25323, 28686, 32524, 36817, 41695
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
The partitions are represented as weakly increasing lists of parts.
|
|
LINKS
|
|
|
EXAMPLE
|
There are a(13) = 23 such partitions of 13:
01: [ 1 2 3 7 ]
02: [ 1 2 4 6 ]
03: [ 1 2 5 5 ]
04: [ 1 2 10 ]
05: [ 1 3 3 6 ]
06: [ 1 3 4 5 ]
07: [ 1 3 9 ]
08: [ 1 4 4 4 ]
09: [ 1 4 8 ]
10: [ 1 5 7 ]
11: [ 1 6 6 ]
12: [ 1 12 ]
13: [ 2 3 8 ]
14: [ 2 4 7 ]
15: [ 2 5 6 ]
16: [ 2 11 ]
17: [ 3 4 6 ]
18: [ 3 5 5 ]
19: [ 3 10 ]
20: [ 4 9 ]
21: [ 5 8 ]
22: [ 6 7 ]
23: [ 13 ]
|
|
CROSSREFS
|
Cf. A238861 (compositions with superdiagonal growth), A000009 (partitions into distinct parts have superdiagonal growth by definition).
Cf. A238859 (compositions of n with subdiagonal growth), A238876 (partitions with subdiagonal growth), A001227 (partitions into distinct parts with subdiagonal growth).
Cf. A008930 (subdiagonal compositions), A238875 (subdiagonal partitions), A010054 (subdiagonal partitions into distinct parts).
Cf. A219282 (superdiagonal compositions), A238873 (superdiagonal partitions), A238394 (strictly superdiagonal partitions), A238874 (strictly superdiagonal compositions), A025147 (strictly superdiagonal partitions into distinct parts).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|