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%I #8 Jun 07 2019 16:33:38
%S 1,1,1,1,2,3,2,4,4,4,5,7,5,11,12,11,12,20,15,24,22,27,28,37,28,45,43,
%T 48,50,66,58,79,72,84,87,112,106,135,128,158,147,186,180,218,220,265,
%U 246,304,303,354,340,412,418,471,463,538,543,642,600,711,755
%N Number of reversed integer partitions y of n such that the k-th differences of y are distinct for all k >= 0 and are disjoint from the i-th differences for i != k.
%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 A325405.
%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(12) = 5 reversed partitions (A = 10, B = 11, C = 12):
%e (1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C)
%e (13) (14) (15) (16) (17) (18) (19) (29) (39)
%e (23) (25) (26) (27) (28) (38) (57)
%e (34) (35) (45) (37) (47) (1B)
%e (46) (56) (2A)
%e (1A)
%e (146)
%t Table[Length[Select[Reverse/@IntegerPartitions[n],UnsameQ@@Join@@Table[Differences[#,k],{k,0,Length[#]}]&]],{n,0,30}]
%Y Cf. A279945, A325325, A325349, A325353, A325354, A325365, A325368, A325391, A325393, A325405, A325406, A325468.
%K nonn
%O 0,5
%A _Gus Wiseman_, May 02 2019
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