cp's OEIS Frontend

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

%I A238876 #15 Mar 31 2014 02:08:20
%S A238876 1,1,2,3,4,6,8,10,15,20,24,34,46,58,76,97,126,166,209,262,333,422,529,
%T A238876 667,833,1024,1268,1567,1934,2385,2911,3549,4319,5237,6340,7675,9274,
%U A238876 11164,13404,16046,19173,22889,27278,32458,38574,45750,54140,63976,75449,88848,104503,122773,144077,168860,197609,230916,269494
%N A238876 Partitions with subdiagonal growth: number of partitions (p0, p1, p2, ...) of n with pi - p0 <= i.
%C A238876 The partitions are represented as weakly increasing lists of parts.
%C A238876 The number of such partitions that start with part p0 = 1 are given in A238875.
%H A238876 Alois P. Heinz, <a href="/A238876/b238876.txt">Table of n, a(n) for n = 0..400</a>
%e A238876 The a(9) = 20 such partitions are:
%e A238876 01:  [ 1 1 1 1 1 1 1 1 1 ]
%e A238876 02:  [ 1 1 1 1 1 1 1 2 ]
%e A238876 03:  [ 1 1 1 1 1 1 3 ]
%e A238876 04:  [ 1 1 1 1 1 2 2 ]
%e A238876 05:  [ 1 1 1 1 1 4 ]
%e A238876 06:  [ 1 1 1 1 2 3 ]
%e A238876 07:  [ 1 1 1 1 5 ]
%e A238876 08:  [ 1 1 1 2 2 2 ]
%e A238876 09:  [ 1 1 1 2 4 ]
%e A238876 10:  [ 1 1 1 3 3 ]
%e A238876 11:  [ 1 1 2 2 3 ]
%e A238876 12:  [ 1 1 3 4 ]
%e A238876 13:  [ 1 2 2 2 2 ]
%e A238876 14:  [ 1 2 2 4 ]
%e A238876 15:  [ 1 2 3 3 ]
%e A238876 16:  [ 2 2 2 3 ]
%e A238876 17:  [ 2 3 4 ]
%e A238876 18:  [ 3 3 3 ]
%e A238876 19:  [ 4 5 ]
%e A238876 20:  [ 9 ]
%Y A238876 Cf. A238859 (compositions with subdiagonal growth), A001227 (partitions into distinct parts with subdiagonal growth).
%Y A238876 Cf. A238860 (partitions with superdiagonal growth), A238861 (compositions with superdiagonal growth), A000009 (partitions into distinct parts have superdiagonal growth by definition).
%Y A238876 Cf. A008930 (subdiagonal compositions), A010054 (subdiagonal partitions into distinct parts).
%Y A238876 Cf. A219282 (superdiagonal compositions), A238873 (superdiagonal partitions), A238394 (strictly superdiagonal partitions), A238874 (strictly superdiagonal compositions), A025147 (strictly superdiagonal partitions into distinct parts).
%K A238876 nonn
%O A238876 0,3
%A A238876 _Joerg Arndt_, Mar 24 2014