A238860 Partitions with superdiagonal growth: number of partitions (p0, p1, p2, ...) of n with pi - p0 >= i.

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

Author

Joerg Arndt, Mar 24 2014

Keywords

• nonn

Comments

The partitions are represented as weakly increasing lists of parts.

Examples

			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 ]
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400

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).