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A325680 Number of compositions of n such that every distinct circular subsequence has a different sum. 13
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 (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..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

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Last modified February 2 06:48 EST 2023. Contains 360000 sequences. (Running on oeis4.)