OFFSET
0,4
COMMENTS
A composition of n is a finite sequence of positive integers summing to n.
LINKS
EXAMPLE
The a(0) = 1 through a(5) = 5 splits:
() (1) (2) (3) (4) (5)
(12) (13) (14)
(21) (31) (23)
(1)(2) (1)(3) (32)
(2)(1) (3)(1) (41)
(1)(4)
(2)(3)
(3)(2)
(4)(1)
The a(6) = 29 splits:
(6) (1)(5) (1)(2)(3)
(15) (2)(4) (1)(3)(2)
(24) (4)(2) (2)(1)(3)
(42) (5)(1) (2)(3)(1)
(51) (1)(23) (3)(1)(2)
(123) (1)(32) (3)(2)(1)
(132) (13)(2)
(213) (2)(13)
(231) (2)(31)
(312) (23)(1)
(321) (31)(2)
(32)(1)
MATHEMATICA
splits[dom_]:=Append[Join@@Table[Prepend[#, Take[dom, i]]&/@splits[Drop[dom, i]], {i, Length[dom]-1}], {dom}];
Table[Sum[Length[Select[splits[ctn], UnsameQ@@Total/@#&]], {ctn, Join@@Permutations/@Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 0, 15}]
CROSSREFS
The version with equal instead of different sums is A336130.
Starting with a non-strict composition gives A336127.
Starting with a partition gives A336131.
Starting with a strict partition gives A336132.
Partitions of partitions are A001970.
Partitions of compositions are A075900.
Compositions of compositions are A133494.
Set partitions with distinct block-sums are A275780.
Compositions of partitions are A323583.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 10 2020
EXTENSIONS
a(31)-a(50) from Max Alekseyev, Feb 14 2024
STATUS
approved