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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

Table of n, a(n) for n=0..43.

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.)