%I #15 Mar 31 2014 02:08:20

%S 1,1,2,3,4,6,8,10,15,20,24,34,46,58,76,97,126,166,209,262,333,422,529,

%T 667,833,1024,1268,1567,1934,2385,2911,3549,4319,5237,6340,7675,9274,

%U 11164,13404,16046,19173,22889,27278,32458,38574,45750,54140,63976,75449,88848,104503,122773,144077,168860,197609,230916,269494

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

%C The partitions are represented as weakly increasing lists of parts.

%C The number of such partitions that start with part p0 = 1 are given in A238875.

%H Alois P. Heinz, <a href="/A238876/b238876.txt">Table of n, a(n) for n = 0..400</a>

%e The a(9) = 20 such partitions are:

%e 01: [ 1 1 1 1 1 1 1 1 1 ]

%e 02: [ 1 1 1 1 1 1 1 2 ]

%e 03: [ 1 1 1 1 1 1 3 ]

%e 04: [ 1 1 1 1 1 2 2 ]

%e 05: [ 1 1 1 1 1 4 ]

%e 06: [ 1 1 1 1 2 3 ]

%e 07: [ 1 1 1 1 5 ]

%e 08: [ 1 1 1 2 2 2 ]

%e 09: [ 1 1 1 2 4 ]

%e 10: [ 1 1 1 3 3 ]

%e 11: [ 1 1 2 2 3 ]

%e 12: [ 1 1 3 4 ]

%e 13: [ 1 2 2 2 2 ]

%e 14: [ 1 2 2 4 ]

%e 15: [ 1 2 3 3 ]

%e 16: [ 2 2 2 3 ]

%e 17: [ 2 3 4 ]

%e 18: [ 3 3 3 ]

%e 19: [ 4 5 ]

%e 20: [ 9 ]

%Y Cf. A238859 (compositions with subdiagonal growth), A001227 (partitions into distinct parts with subdiagonal growth).

%Y Cf. A238860 (partitions with superdiagonal growth), A238861 (compositions with superdiagonal growth), A000009 (partitions into distinct parts have superdiagonal growth by definition).

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

%Y Cf. A219282 (superdiagonal compositions), A238873 (superdiagonal partitions), A238394 (strictly superdiagonal partitions), A238874 (strictly superdiagonal compositions), A025147 (strictly superdiagonal partitions into distinct parts).

%K nonn

%O 0,3

%A _Joerg Arndt_, Mar 24 2014