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%I #4 May 03 2019 21:26:30
%S 1,1,1,2,2,3,3,5,6,6,9,11,10,15,17,19,24,31,26,40,43,51,52,72,66,89,
%T 88,111,119,150,130,183,193,229,231,279,287,358,365,430,426,538,535,
%U 649,680,742,803,943,982,1136,1115
%N Number of integer partitions y of n such that the k-th differences of y are distinct (independently) for all k >= 0.
%C 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 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 The Heinz numbers of these partitions are given by A325467.
%H Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e The a(1) = 1 through a(9) = 6 partitions:
%e (1) (2) (3) (4) (5) (6) (7) (8) (9)
%e (21) (31) (32) (42) (43) (53) (54)
%e (41) (51) (52) (62) (63)
%e (61) (71) (72)
%e (421) (431) (81)
%e (521) (621)
%t Table[Length[Select[IntegerPartitions[n],And@@Table[UnsameQ@@Differences[#,k],{k,0,Length[#]}]&]],{n,0,30}]
%Y Cf. A000009, A325324, A325325, A325349, A325353, A325354, A325391, A325393, A325404, A325406, A325467.
%K nonn
%O 0,4
%A _Gus Wiseman_, May 03 2019
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