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A238873 Number of superdiagonal partitions: partitions (p1, p2, p3, ...) of n such that pi >= i.

%I A238873 #25 Apr 14 2025 08:43:05
%S A238873 1,1,1,2,3,3,5,7,9,11,14,19,25,31,38,46,59,73,92,112,135,162,196,237,
%T A238873 289,349,417,496,587,691,820,970,1151,1357,1598,1870,2183,2537,2952,
%U A238873 3433,3997,4644,5393,6248,7220,8318,9566,10981,12605,14457,16582,19002,21767,24886,28424,32396,36873,41901,47579,53974,61221
%N A238873 Number of superdiagonal partitions: partitions (p1, p2, p3, ...) of n such that pi >= i.
%H A238873 Alois P. Heinz, <a href="/A238873/b238873.txt">Table of n, a(n) for n = 0..1000</a> (first 132 terms from Joerg Arndt)
%H A238873 M. Archibald, A. Blecher, S. Elizalde, and A. Knopfmacher, <a href="https://doi.org/10.1007/s13370-025-01282-0">Subdiagonal and superdiagonal partitions</a>, Afr. Mat. 36, 77 (2025). See p. 5.
%e A238873 The a(13) = 31 such partitions of 13 are:
%e A238873   01:  [ 1 2 3 7 ]
%e A238873   02:  [ 1 2 4 6 ]
%e A238873   03:  [ 1 2 5 5 ]
%e A238873   04:  [ 1 2 10 ]
%e A238873   05:  [ 1 3 3 6 ]
%e A238873   06:  [ 1 3 4 5 ]
%e A238873   07:  [ 1 3 9 ]
%e A238873   08:  [ 1 4 4 4 ]
%e A238873   09:  [ 1 4 8 ]
%e A238873   10:  [ 1 5 7 ]
%e A238873   11:  [ 1 6 6 ]
%e A238873   12:  [ 1 12 ]
%e A238873   13:  [ 2 2 3 6 ]
%e A238873   14:  [ 2 2 4 5 ]
%e A238873   15:  [ 2 2 9 ]
%e A238873   16:  [ 2 3 3 5 ]
%e A238873   17:  [ 2 3 4 4 ]
%e A238873   18:  [ 2 3 8 ]
%e A238873   19:  [ 2 4 7 ]
%e A238873   20:  [ 2 5 6 ]
%e A238873   21:  [ 2 11 ]
%e A238873   22:  [ 3 3 3 4 ]
%e A238873   23:  [ 3 3 7 ]
%e A238873   24:  [ 3 4 6 ]
%e A238873   25:  [ 3 5 5 ]
%e A238873   26:  [ 3 10 ]
%e A238873   27:  [ 4 4 5 ]
%e A238873   28:  [ 4 9 ]
%e A238873   29:  [ 5 8 ]
%e A238873   30:  [ 6 7 ]
%e A238873   31:  [ 13 ]
%Y A238873 Cf. A219282 (superdiagonal compositions), A238394 (strictly superdiagonal partitions), A025147 (strictly superdiagonal partitions into distinct parts).
%Y A238873 Cf. A238875 (subdiagonal partitions), A008930 (subdiagonal compositions), A010054 (subdiagonal partitions into distinct parts).
%Y A238873 Cf. A238859 (compositions of n with subdiagonal growth), A238876 (partitions with subdiagonal growth), A001227 (partitions into distinct parts with subdiagonal growth).
%Y A238873 Cf. A238860 (partitions with superdiagonal growth), A238861 (compositions with superdiagonal growth), A000009 (partitions into distinct parts have superdiagonal growth by definition).
%K A238873 nonn
%O A238873 0,4
%A A238873 _Joerg Arndt_, Mar 23 2014