

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
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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



