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A325680 Number of compositions of n such that every distinct circular subsequence has a different sum. 6
1, 1, 2, 4, 5, 6, 8, 14, 16, 29, 24, 42, 46, 78, 66, 146, 133, 242 (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.

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..17.

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

STATUS

approved

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Last modified December 8 09:32 EST 2019. Contains 329862 sequences. (Running on oeis4.)