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 A325875 Number of compositions of n whose differences of all degrees > 1 are nonzero. 7
 1, 1, 2, 3, 7, 13, 20, 38, 69, 129, 222, 407, 726, 1313, 2318, 4146, 7432, 13296, 23759, 42458, 75714 (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 are the sequence itself, while k-th differences for k > 0 are the differences of the (k-1)-th differences. If m is the length of the sequence, its differences of all degrees are the union of the zeroth through m-th differences. A composition of n is a finite sequence of positive integers with sum n. The case for all degrees including 1 is A325851. LINKS EXAMPLE The a(1) = 1 through a(6) = 20 compositions:   (1)  (2)   (3)   (4)    (5)     (6)        (11)  (12)  (13)   (14)    (15)              (21)  (22)   (23)    (24)                    (31)   (32)    (33)                    (112)  (41)    (42)                    (121)  (113)   (51)                    (211)  (122)   (114)                           (131)   (132)                           (212)   (141)                           (221)   (213)                           (311)   (231)                           (1121)  (312)                           (1211)  (411)                                   (1122)                                   (1131)                                   (1212)                                   (1311)                                   (2121)                                   (2211)                                   (11211) MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !MemberQ[Union@@Table[Differences[#, i], {i, 2, Length[#]}], 0]&]], {n, 0, 10}] CROSSREFS Cf. A049988, A238423, A325325, A325468, A325545, A325849, A325850, A325851, A325852, A325874, A325876. Sequence in context: A156300 A067834 A070754 * A049887 A048216 A003509 Adjacent sequences:  A325872 A325873 A325874 * A325876 A325877 A325878 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 02 2019 STATUS approved

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Last modified April 6 11:51 EDT 2020. Contains 333273 sequences. (Running on oeis4.)