login
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
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.
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}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 13 2019
EXTENSIONS
a(18)-a(25) from Robert Price, Jun 19 2021
STATUS
approved