A325849 Number of strict compositions of n with no three consecutive parts in arithmetic progression.

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

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: A279375 A245143 A350393 * A104220 A321986 A325187

Adjacent sequences: A325846 A325847 A325848 * A325850 A325851 A325852

Keyword

nonn

Author

Gus Wiseman, May 31 2019

Status

approved