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 A325358 Number of integer partitions of n whose augmented differences are strictly decreasing. 10
 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 6, 7, 9, 10, 11, 13, 14, 15, 18, 20, 21, 24, 26, 28, 33, 36, 38, 43, 46, 49, 56, 60, 63, 71, 76, 80, 90, 96, 100, 112, 120, 125, 139, 149, 155, 171, 183, 190, 208, 223, 232, 252, 269, 280, 304, 325, 338, 364, 387, 403 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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 A325396. LINKS Fausto A. C. Cariboni, Table of n, a(n) for n = 0..1000 EXAMPLE The a(1) = 1 through a(11) = 6 partitions:   (1)  (2)  (3)   (4)   (5)   (6)   (7)    (8)    (9)    (10)   (11)             (21)  (31)  (41)  (42)  (52)   (62)   (63)   (73)   (83)                               (51)  (61)   (71)   (72)   (82)   (92)                                     (421)  (521)  (81)   (91)   (101)                                                   (621)  (631)  (731)                                                          (721)  (821) MATHEMATICA aug[y_]:=Table[If[i

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Last modified July 24 06:56 EDT 2021. Contains 346273 sequences. (Running on oeis4.)