cp's OEIS Frontend

A325393 Number of integer partitions of n whose k-th differences are strictly decreasing for all k >= 0.

%I A325393 #6 May 03 2019 08:36:49
%S A325393 1,1,1,2,2,3,3,4,5,5,6,8,7,9,11,10,12,15,13,16,19,18,20,24,22,26,29,
%T A325393 28,31,37,33,38,43,42,44,52,48,55,59,58,62,72,65,74,80,80,82,94,88,99,
%U A325393 103,104,108,123,114,126,133,135,137,155,145,161,166,169,174
%N A325393 Number of integer partitions of n whose k-th differences are strictly decreasing for all k >= 0.
%C A325393 The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) are (-3,-2).
%C A325393 The zeroth differences of a sequence are the sequence itself, while the k-th differences for k > 0 are the differences of the (k-1)-th differences.
%C A325393 The Heinz numbers of these partitions are given by A325399.
%H A325393 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325393 The a(1) = 1 through a(9) = 5 partitions:
%e A325393   (1)  (2)  (3)   (4)   (5)   (6)   (7)   (8)    (9)
%e A325393             (21)  (31)  (32)  (42)  (43)  (53)   (54)
%e A325393                         (41)  (51)  (52)  (62)   (63)
%e A325393                                     (61)  (71)   (72)
%e A325393                                           (431)  (81)
%t A325393 Table[Length[Select[IntegerPartitions[n],And@@Table[Greater@@Differences[#,k],{k,0,Length[#]}]&]],{n,0,30}]
%Y A325393 Cf. A049988, A320466, A325353, A325354, A325358, A325391, A325396, A325399, A325404, A325406, A325457, A325468.
%K A325393 nonn
%O A325393 0,4
%A A325393 _Gus Wiseman_, May 02 2019