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A238876
Partitions with subdiagonal growth: number of partitions (p0, p1, p2, ...) of n with pi - p0 <= i.
9
1, 1, 2, 3, 4, 6, 8, 10, 15, 20, 24, 34, 46, 58, 76, 97, 126, 166, 209, 262, 333, 422, 529, 667, 833, 1024, 1268, 1567, 1934, 2385, 2911, 3549, 4319, 5237, 6340, 7675, 9274, 11164, 13404, 16046, 19173, 22889, 27278, 32458, 38574, 45750, 54140, 63976, 75449, 88848, 104503, 122773, 144077, 168860, 197609, 230916, 269494
OFFSET
0,3
COMMENTS
The partitions are represented as weakly increasing lists of parts.
The number of such partitions that start with part p0 = 1 are given in A238875.
LINKS
EXAMPLE
The a(9) = 20 such partitions are:
01: [ 1 1 1 1 1 1 1 1 1 ]
02: [ 1 1 1 1 1 1 1 2 ]
03: [ 1 1 1 1 1 1 3 ]
04: [ 1 1 1 1 1 2 2 ]
05: [ 1 1 1 1 1 4 ]
06: [ 1 1 1 1 2 3 ]
07: [ 1 1 1 1 5 ]
08: [ 1 1 1 2 2 2 ]
09: [ 1 1 1 2 4 ]
10: [ 1 1 1 3 3 ]
11: [ 1 1 2 2 3 ]
12: [ 1 1 3 4 ]
13: [ 1 2 2 2 2 ]
14: [ 1 2 2 4 ]
15: [ 1 2 3 3 ]
16: [ 2 2 2 3 ]
17: [ 2 3 4 ]
18: [ 3 3 3 ]
19: [ 4 5 ]
20: [ 9 ]
CROSSREFS
Cf. A238859 (compositions with subdiagonal growth), A001227 (partitions into distinct parts with subdiagonal growth).
Cf. A238860 (partitions with superdiagonal growth), A238861 (compositions with superdiagonal growth), A000009 (partitions into distinct parts have superdiagonal growth by definition).
Cf. A008930 (subdiagonal compositions), 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: A375186 A297417 A343502 * A211856 A066816 A247334
KEYWORD
nonn
AUTHOR
Joerg Arndt, Mar 24 2014
STATUS
approved