A336131 Number of ways to split an integer partition of n into contiguous subsequences all having different sums.

1, 1, 2, 6, 9, 20, 44, 74, 123, 231, 441, 681, 1188, 1889, 3110, 5448, 8310, 13046

Offset: 0

Author

Gus Wiseman, Jul 11 2020

Keywords

• nonn
• more

Examples

			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)
		

Links

• Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.

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.

Cf. A006951, A063834, A279786, A305551, A316245, A323433, A336130, A336134, A336135.

Programs

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}]