A238876 Partitions with subdiagonal growth: number of partitions (p0, p1, p2, ...) of n with pi - p0 <= i.

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

Author

Joerg Arndt, Mar 24 2014

Keywords

• nonn

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.

Examples

			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 ]
		

Links

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

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).