A325680 Number of compositions of n such that every distinct circular subsequence has a different sum.

1, 1, 2, 4, 5, 6, 8, 14, 16, 29, 24, 42, 46, 78, 66, 146, 133, 242, 208, 386, 352, 620, 494, 948, 842, 1447

Offset

0,3

Comments

A composition of n is a finite sequence of positive integers summing to n.

A circular subsequence is a sequence of consecutive terms where the first and last parts are also considered consecutive.

Links

Table of n, a(n) for n=0..25.

Example

The a(1) = 1 through a(8) = 16 compositions:
  (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)
       (11)  (12)   (13)    (14)     (15)      (16)       (17)
             (21)   (22)    (23)     (24)      (25)       (26)
             (111)  (31)    (32)     (33)      (34)       (35)
                    (1111)  (41)     (42)      (43)       (44)
                            (11111)  (51)      (52)       (53)
                                     (222)     (61)       (62)
                                     (111111)  (124)      (71)
                                               (142)      (125)
                                               (214)      (152)
                                               (241)      (215)
                                               (412)      (251)
                                               (421)      (512)
                                               (1111111)  (521)
                                                          (2222)
                                                          (11111111)

Mathematica

subalt[q_]:=Union[ReplaceList[q, {___, s__, ___}:>{s}], DeleteCases[ReplaceList[q, {t___, __, u___}:>{u, t}], {}]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@Total/@subalt[#]&]], {n, 0, 15}]

Crossrefs

Cf. A000079, A008965, A108917, A143823, A169942, A276024.

Cf. A325545, A325676, A325682, A325685, A325687, A325688.

Sequence in context: A270877 A303909 A110277 * A176654 A185867 A326910

Adjacent sequences: A325677 A325678 A325679 * A325681 A325682 A325683

Keyword

nonn,more

Author

Gus Wiseman, May 13 2019

Extensions

a(18)-a(25) from Robert Price, Jun 19 2021

Status

approved