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 A325849 Number of strict compositions of n with no three consecutive parts in arithmetic progression. 6
 1, 1, 1, 3, 3, 5, 9, 13, 19, 23, 51, 57, 91, 117, 179, 283, 381, 531, 737, 1017, 1335, 2259, 2745, 3983, 5289, 7367, 9413, 13155, 19461, 25129, 33997, 45633, 61225, 80481, 107091, 137475, 205243, 253997, 345527, 447003, 604919, 768331, 1026167, 1299227 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A composition of n is a finite sequence of positive integers with sum n. a(n) is the number of strict compositions of n with no two of their adjacent first-differences equal, or with no 0's in their second-differences. LINKS Wikipedia, Arithmetic progression EXAMPLE The a(1) = 1 through a(8) = 19 compositions:   (1)  (2)  (3)   (4)   (5)   (6)    (7)    (8)             (12)  (13)  (14)  (15)   (16)   (17)             (21)  (31)  (23)  (24)   (25)   (26)                         (32)  (42)   (34)   (35)                         (41)  (51)   (43)   (53)                               (132)  (52)   (62)                               (213)  (61)   (71)                               (231)  (124)  (125)                               (312)  (142)  (134)                                      (214)  (143)                                      (241)  (152)                                      (412)  (215)                                      (421)  (251)                                             (314)                                             (341)                                             (413)                                             (431)                                             (512)                                             (521) MATHEMATICA Table[Length[Select[Join@@Permutations/@Select[IntegerPartitions[n], UnsameQ@@#&], !MemberQ[Differences[#, 2], 0]&]], {n, 0, 30}] CROSSREFS The non-strict case is A238423. Cf. A007862, A049988, A175342, A279945, A295370, A325545, A325874, A325875. Sequence in context: A317142 A279375 A245143 * A104220 A321986 A325187 Adjacent sequences:  A325846 A325847 A325848 * A325850 A325851 A325852 KEYWORD nonn AUTHOR Gus Wiseman, May 31 2019 STATUS approved

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Last modified February 25 11:39 EST 2020. Contains 332233 sequences. (Running on oeis4.)