OFFSET
0,3
COMMENTS
A composition of n is a finite sequence of positive integers with sum n.
EXAMPLE
The a(1) = 1 through a(7) = 20 compositions:
(1) (2) (3) (4) (5) (6) (7)
(11) (111) (22) (113) (33) (115)
(112) (122) (114) (133)
(211) (221) (222) (223)
(1111) (311) (411) (322)
(1112) (1113) (331)
(2111) (3111) (511)
(11111) (11112) (1114)
(21111) (1222)
(111111) (2221)
(4111)
(11113)
(11122)
(22111)
(31111)
(111112)
(111211)
(112111)
(211111)
(1111111)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@Length/@Split[#]&]], {n, 0, 10}]
CROSSREFS
The normal case is A329740.
The case of partitions is A098859.
Strict compositions are A032020.
Compositions with relatively prime run-lengths are A000740.
Compositions with distinct multiplicities are A242882.
Compositions with distinct differences are A325545.
Compositions with equal run-lengths are A329738.
Compositions with normal run-lengths are A329766.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 20 2019
EXTENSIONS
a(21)-a(26) from Giovanni Resta, Nov 22 2019
a(27)-a(43) from Alois P. Heinz, Jul 06 2020
STATUS
approved