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%I #7 May 03 2019 08:35:59
%S 1,1,1,2,2,3,3,5,5,6,8,9,9,13,13,15,19,20,20,28,28,30,36,40,40,50,50,
%T 56,64,68,68,86,86,92,102,112,114,133,133,146,158,173,173,202,202,215,
%U 237,256,256,287,287,324,340,359,359,403,423,446,464,495,495
%N Number of reversed integer partitions of n whose k-th differences are strictly increasing 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 A325398.
%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 reversed partitions:
%e (1) (2) (3) (4) (5) (6) (7) (8) (9)
%e (12) (13) (14) (15) (16) (17) (18)
%e (23) (24) (25) (26) (27)
%e (34) (35) (36)
%e (124) (125) (45)
%e (126)
%e The smallest reversed strict partition with strictly increasing differences not counted by this sequence is (1,2,4,7), whose first and second differences are (1,2,3) and (1,1) respectively.
%t Table[Length[Select[Reverse/@IntegerPartitions[n],And@@Table[Less@@Differences[#,k],{k,0,Length[#]}]&]],{n,0,30}]
%Y Cf. A179254, A240026, A325353, A325354, A325357, A325393, A325395, A325398, A325404, A325406, A325456, A325468.
%K nonn
%O 0,4
%A _Gus Wiseman_, May 02 2019
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