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 A329136 Number of integer partitions of n whose augmented differences are an aperiodic word. 7
 1, 1, 1, 2, 4, 5, 10, 14, 19, 28, 40, 53, 75, 99, 131, 172, 226, 294, 380, 488, 617, 787, 996, 1250, 1565, 1953, 2425, 3003, 3705, 4559, 5589, 6836, 8329, 10132, 12292, 14871, 17950, 21629, 25988, 31169, 37306, 44569, 53139, 63247, 75133, 89111, 105515, 124737 (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). A sequence is aperiodic if its cyclic rotations are all different. LINKS FORMULA a(n) + A329143(n) = A000041(n). EXAMPLE The a(1) = 1 through a(7) = 14 partitions:   (1)  (2)  (3)    (4)      (5)        (6)          (7)             (2,1)  (2,2)    (4,1)      (3,3)        (4,3)                    (3,1)    (2,2,1)    (4,2)        (5,2)                    (2,1,1)  (3,1,1)    (5,1)        (6,1)                             (2,1,1,1)  (2,2,2)      (3,2,2)                                        (3,2,1)      (3,3,1)                                        (4,1,1)      (4,2,1)                                        (2,2,1,1)    (5,1,1)                                        (3,1,1,1)    (2,2,2,1)                                        (2,1,1,1,1)  (3,2,1,1)                                                     (4,1,1,1)                                                     (2,2,1,1,1)                                                     (3,1,1,1,1)                                                     (2,1,1,1,1,1) With augmented differences:   (1)  (2)  (3)    (4)      (5)        (6)          (7)             (2,1)  (1,2)    (4,1)      (1,3)        (2,3)                    (3,1)    (1,2,1)    (3,2)        (4,2)                    (2,1,1)  (3,1,1)    (5,1)        (6,1)                             (2,1,1,1)  (1,1,2)      (1,3,1)                                        (2,2,1)      (2,1,2)                                        (4,1,1)      (3,2,1)                                        (1,2,1,1)    (5,1,1)                                        (3,1,1,1)    (1,1,2,1)                                        (2,1,1,1,1)  (2,2,1,1)                                                     (4,1,1,1)                                                     (1,2,1,1,1)                                                     (3,1,1,1,1)                                                     (2,1,1,1,1,1) MATHEMATICA aperQ[q_]:=Array[RotateRight[q, #1]&, Length[q], 1, UnsameQ]; aug[y_]:=Table[If[i

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Last modified December 2 05:01 EST 2021. Contains 349437 sequences. (Running on oeis4.)