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

Author

Joerg Arndt, Mar 23 2014

Keywords

• nonn

Examples

			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 ]
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 132 terms from Joerg Arndt)
• M. Archibald, A. Blecher, S. Elizalde, and A. Knopfmacher, Subdiagonal and superdiagonal partitions, Afr. Mat. 36, 77 (2025). See p. 5.

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).