A238873 Number of superdiagonal partitions: partitions (p1, p2, p3, ...) of n such that pi >= i.

1, 1, 1, 2, 3, 3, 5, 7, 9, 11, 14, 19, 25, 31, 38, 46, 59, 73, 92, 112, 135, 162, 196, 237, 289, 349, 417, 496, 587, 691, 820, 970, 1151, 1357, 1598, 1870, 2183, 2537, 2952, 3433, 3997, 4644, 5393, 6248, 7220, 8318, 9566, 10981, 12605, 14457, 16582, 19002, 21767, 24886, 28424, 32396, 36873, 41901, 47579, 53974, 61221

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 132 terms from Joerg Arndt)

Example

The a(13) = 31 such partitions of 13 are:
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 2 3 6 ]
14:  [ 2 2 4 5 ]
15:  [ 2 2 9 ]
16:  [ 2 3 3 5 ]
17:  [ 2 3 4 4 ]
18:  [ 2 3 8 ]
19:  [ 2 4 7 ]
20:  [ 2 5 6 ]
21:  [ 2 11 ]
22:  [ 3 3 3 4 ]
23:  [ 3 3 7 ]
24:  [ 3 4 6 ]
25:  [ 3 5 5 ]
26:  [ 3 10 ]
27:  [ 4 4 5 ]
28:  [ 4 9 ]
29:  [ 5 8 ]
30:  [ 6 7 ]
31:  [ 13 ]

Crossrefs

Cf. A219282 (superdiagonal compositions), A238394 (strictly superdiagonal partitions), A025147 (strictly superdiagonal partitions into distinct parts).

Cf. A238875 (subdiagonal partitions), A008930 (subdiagonal compositions), A010054 (subdiagonal partitions into distinct parts).

Cf. A238859 (compositions of n with subdiagonal growth), A238876 (partitions 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).

Sequence in context: A030779 A030729 A111865 * A042955 A035553 A108961

Adjacent sequences: A238870 A238871 A238872 * A238874 A238875 A238876

Keyword

nonn

Author

Joerg Arndt, Mar 23 2014

Status

approved