OFFSET
0,3
LINKS
EXAMPLE
The a(1) = 1 through a(4) = 9 splits:
(1) (2) (3) (4)
(1,1) (2,1) (2,2)
(1,1,1) (3,1)
(2),(1) (2,1,1)
(1),(1,1) (3),(1)
(1,1),(1) (1,1,1,1)
(2,1),(1)
(1),(1,1,1)
(1,1,1),(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, IntegerPartitions[n]}], {n, 0, 10}]
CROSSREFS
The version with equal instead of different sums is A317715.
Starting with a composition gives A336127.
Starting with a strict composition gives A336128.
Starting with a strict partition gives A336132.
Partitions of partitions are A001970.
Partitions of compositions are A075900.
Compositions of compositions are A133494.
Compositions of partitions are A323583.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 11 2020
STATUS
approved