login
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
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).
Sequence in context: A356607 A366843 A370805 * A144367 A370778 A075465
KEYWORD
nonn
AUTHOR
Joerg Arndt, Mar 24 2014
STATUS
approved