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

0,3

Links

Table of n, a(n) for n=0..17.

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

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.

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

Sequence in context: A088902 A265016 A279897 * A095967 A316429 A337639

Adjacent sequences: A336128 A336129 A336130 * A336132 A336133 A336134

Keyword

nonn,more

Author

Gus Wiseman, Jul 11 2020

Status

approved