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 A325552 Number of compositions of n with distinct differences up to sign. 6
 1, 1, 2, 3, 6, 9, 12, 23, 38, 61, 78, 135, 194, 315, 454, 699, 982, 1495, 2102, 3085, 4406, 6583, 9048, 13117, 18540, 26399 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A composition of n is a finite sequence of positive integers summing to n. The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (3,1,2) are (-2,1). a(n) has the same parity as n for n > 0, since reversing a composition does not change whether or not it has this property, and the only valid symmetric compositions are (n) and (n/2,n/2), with the latter only existing for even n. - Charlie Neder, Jun 06 2019 LINKS EXAMPLE The differences of (1,2,1) are (1,-1), which are different but not up to sign, so (1,2,1) is not counted under a(4). The a(1) = 1 through a(7) = 23 compositions:   (1)  (2)   (3)   (4)    (5)    (6)    (7)        (11)  (12)  (13)   (14)   (15)   (16)              (21)  (22)   (23)   (24)   (25)                    (31)   (32)   (33)   (34)                    (112)  (41)   (42)   (43)                    (211)  (113)  (51)   (52)                           (122)  (114)  (61)                           (221)  (132)  (115)                           (311)  (213)  (124)                                  (231)  (133)                                  (312)  (142)                                  (411)  (214)                                         (223)                                         (241)                                         (322)                                         (331)                                         (412)                                         (421)                                         (511)                                         (1132)                                         (2113)                                         (2311)                                         (3112) MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@Abs[Differences[#]]&]], {n, 0, 15}] CROSSREFS Cf. A000079, A070211, A175342, A242882, A325325, A325368, A325404, A325545, A325551, A325553, A325555, A325557. Sequence in context: A058616 A298435 A261539 * A271882 A123316 A303365 Adjacent sequences:  A325549 A325550 A325551 * A325553 A325554 A325555 KEYWORD nonn,more AUTHOR Gus Wiseman, May 11 2019 STATUS approved

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Last modified January 19 00:40 EST 2020. Contains 331030 sequences. (Running on oeis4.)