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A238860 Partitions with superdiagonal growth: number of partitions (p0, p1, p2, ...) of n with pi - p0 >= i.

%I A238860 #14 Mar 31 2014 02:09:42
%S A238860 1,1,1,2,2,3,4,6,6,9,11,15,18,23,26,35,43,53,64,79,91,113,135,166,197,
%T A238860 237,277,331,387,459,541,646,754,888,1032,1204,1395,1626,1882,2196,
%U A238860 2542,2952,3404,3934,4507,5182,5935,6812,7800,8947,10225,11709,13354,15231,17314,19685,22316,25323,28686,32524,36817,41695
%N A238860 Partitions with superdiagonal growth: number of partitions (p0, p1, p2, ...) of n with pi - p0 >= i.
%C A238860 The partitions are represented as weakly increasing lists of parts.
%H A238860 Alois P. Heinz, <a href="/A238860/b238860.txt">Table of n, a(n) for n = 0..400</a>
%e A238860 There are a(13) = 23 such partitions of 13:
%e A238860 01:  [ 1 2 3 7 ]
%e A238860 02:  [ 1 2 4 6 ]
%e A238860 03:  [ 1 2 5 5 ]
%e A238860 04:  [ 1 2 10 ]
%e A238860 05:  [ 1 3 3 6 ]
%e A238860 06:  [ 1 3 4 5 ]
%e A238860 07:  [ 1 3 9 ]
%e A238860 08:  [ 1 4 4 4 ]
%e A238860 09:  [ 1 4 8 ]
%e A238860 10:  [ 1 5 7 ]
%e A238860 11:  [ 1 6 6 ]
%e A238860 12:  [ 1 12 ]
%e A238860 13:  [ 2 3 8 ]
%e A238860 14:  [ 2 4 7 ]
%e A238860 15:  [ 2 5 6 ]
%e A238860 16:  [ 2 11 ]
%e A238860 17:  [ 3 4 6 ]
%e A238860 18:  [ 3 5 5 ]
%e A238860 19:  [ 3 10 ]
%e A238860 20:  [ 4 9 ]
%e A238860 21:  [ 5 8 ]
%e A238860 22:  [ 6 7 ]
%e A238860 23:  [ 13 ]
%Y A238860 Cf. A238861 (compositions with superdiagonal growth), A000009 (partitions into distinct parts have superdiagonal growth by definition).
%Y A238860 Cf. A238859 (compositions of n with subdiagonal growth), A238876 (partitions with subdiagonal growth), A001227 (partitions into distinct parts with subdiagonal growth).
%Y A238860 Cf. A008930 (subdiagonal compositions), A238875 (subdiagonal partitions), A010054 (subdiagonal partitions into distinct parts).
%Y A238860 Cf. A219282 (superdiagonal compositions), A238873 (superdiagonal partitions), A238394 (strictly superdiagonal partitions), A238874 (strictly superdiagonal compositions), A025147 (strictly superdiagonal partitions into distinct parts).
%K A238860 nonn
%O A238860 0,4
%A A238860 _Joerg Arndt_, Mar 24 2014