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 A325356 Number of integer partitions of n whose augmented differences are weakly increasing. 13
 1, 1, 2, 2, 3, 3, 4, 3, 6, 5, 5, 6, 8, 6, 10, 9, 8, 10, 13, 10, 15, 14, 13, 15, 21, 15, 19, 21, 20, 25, 25, 20, 31, 30, 30, 32, 35, 28, 40, 44, 36, 42, 50, 43, 54, 53, 49, 57, 67, 58, 68, 66, 66, 78, 84, 71, 86, 92, 82, 99, 109 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The augmented differences aug(y) of an integer partition y of length k are given by aug(y)_i = y_i - y_{i + 1} + 1 if i < k and aug(y)_k = y_k. For example, aug(6,5,5,3,3,3) = (2,1,3,1,1,3). The Heinz numbers of these partitions are given by A325394. LINKS EXAMPLE The a(1) = 1 through a(8) = 6 partitions:   (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)        (11)  (111)  (22)    (32)     (33)      (43)       (44)                     (1111)  (11111)  (222)     (1111111)  (53)                                      (111111)             (332)                                                           (2222)                                                           (11111111) For example, the augmented differences of (6,6,5,3) are (1,2,3,3), which are weakly increasing, so (6,6,5,3) is counted under a(20). MATHEMATICA aug[y_]:=Table[If[i

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Last modified September 26 21:46 EDT 2020. Contains 337377 sequences. (Running on oeis4.)