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 A325354 Number of reversed integer partitions of n whose k-th differences are weakly increasing for all k. 11
 1, 1, 2, 3, 5, 6, 10, 11, 15, 19, 24, 25, 36, 37, 43, 54, 63, 64, 80, 81, 100, 113, 122, 123, 151, 166, 178, 195, 217, 218, 269, 270, 295, 316, 332, 372, 424, 425, 447, 472, 547, 550, 616, 617, 659, 750, 777, 782, 862, 885, 995, 1032, 1083, 1090, 1176, 1275 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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). 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. The Heinz numbers of these partitions are given by A325400. LINKS EXAMPLE The a(1) = 1 through a(8) = 15 reversed partitions:   (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)        (11)  (12)   (13)    (14)     (15)      (16)       (17)              (111)  (22)    (23)     (24)      (25)       (26)                     (112)   (113)    (33)      (34)       (35)                     (1111)  (1112)   (114)     (115)      (44)                             (11111)  (123)     (124)      (116)                                      (222)     (223)      (125)                                      (1113)    (1114)     (224)                                      (11112)   (11113)    (1115)                                      (111111)  (111112)   (1124)                                                (1111111)  (2222)                                                           (11114)                                                           (111113)                                                           (1111112)                                                           (11111111) MATHEMATICA Table[Length[Select[Sort/@IntegerPartitions[n], And@@Table[OrderedQ[Differences[#, k]], {k, 0, Length[#]}]&]], {n, 0, 30}] CROSSREFS Cf. A007294, A240026, A325353, A325356, A325360, A325362, A325391, A325393, A325394, A325400, A325404, A325406, A325468. Sequence in context: A302539 A322912 A072720 * A298363 A018396 A003238 Adjacent sequences:  A325351 A325352 A325353 * A325355 A325356 A325357 KEYWORD nonn AUTHOR Gus Wiseman, May 02 2019 STATUS approved

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Last modified April 10 06:23 EDT 2020. Contains 333392 sequences. (Running on oeis4.)