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A238873
Number of superdiagonal partitions: partitions (p1, p2, p3, ...) of n such that pi >= i.
8
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
KEYWORD
nonn
AUTHOR
Joerg Arndt, Mar 23 2014
STATUS
approved