OFFSET
0,4
COMMENTS
A strict composition of n is a finite sequence of distinct positive integers summing to n.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..2000
EXAMPLE
The a(1) = 1 through a(5) = 17 splittings:
(1) (2) (3) (4) (5)
(1,2) (1,3) (1,4)
(2,1) (3,1) (2,3)
(1),(2) (1),(3) (3,2)
(2),(1) (3),(1) (4,1)
(1),(1,2) (1),(4)
(1),(2,1) (2),(3)
(1,2),(1) (3),(2)
(2,1),(1) (4),(1)
(1),(1,3)
(1,2),(2)
(1),(3,1)
(1,3),(1)
(2),(1,2)
(2,1),(2)
(2),(2,1)
(3,1),(1)
MATHEMATICA
strs[n_]:=Join@@Permutations/@Select[IntegerPartitions[n], UnsameQ@@#&];
Table[Length[Join@@Table[Tuples[strs/@ctn], {ctn, strs[n]}]], {n, 0, 15}]
CROSSREFS
The version for partitions is A063834.
Row sums of A072574.
The version for non-strict compositions is A133494.
The version for strict partitions is A279785.
Multiset partitions of partitions are A001970.
Strict compositions are A032020.
Taking a composition of each part of a partition: A075900.
Taking a composition of each part of a strict partition: A304961.
Taking a strict composition of each part of a composition: A307068.
Splittings of partitions are A323583.
Compositions of parts of strict compositions are A336127.
Set partitions of strict compositions are A336140.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2020
STATUS
approved