cp's OEIS Frontend

A325391 Number of reversed integer partitions of n whose k-th differences are strictly increasing for all k >= 0.

%I A325391 #7 May 03 2019 08:35:59
%S A325391 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 A325391 56,64,68,68,86,86,92,102,112,114,133,133,146,158,173,173,202,202,215,
%U A325391 237,256,256,287,287,324,340,359,359,403,423,446,464,495,495
%N A325391 Number of reversed integer partitions of n whose k-th differences are strictly increasing for all k >= 0.
%C A325391 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 A325391 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 A325391 The Heinz numbers of these partitions are given by A325398.
%H A325391 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325391 The a(1) = 1 through a(9) = 6 reversed partitions:
%e A325391   (1)  (2)  (3)   (4)   (5)   (6)   (7)    (8)    (9)
%e A325391             (12)  (13)  (14)  (15)  (16)   (17)   (18)
%e A325391                         (23)  (24)  (25)   (26)   (27)
%e A325391                                     (34)   (35)   (36)
%e A325391                                     (124)  (125)  (45)
%e A325391                                                   (126)
%e A325391 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 A325391 Table[Length[Select[Reverse/@IntegerPartitions[n],And@@Table[Less@@Differences[#,k],{k,0,Length[#]}]&]],{n,0,30}]
%Y A325391 Cf. A179254, A240026, A325353, A325354, A325357, A325393, A325395, A325398, A325404, A325406, A325456, A325468.
%K A325391 nonn
%O A325391 0,4
%A A325391 _Gus Wiseman_, May 02 2019