A336130 Number of ways to split a strict composition of n into contiguous subsequences all having the same sum.

1, 1, 1, 3, 3, 5, 15, 13, 23, 27, 73, 65, 129, 133, 241, 375, 519, 617, 1047, 1177, 1859, 2871, 3913, 4757, 7653, 8761, 13273, 16155, 28803, 30461, 50727, 55741, 87743, 100707, 152233, 168425, 308937, 315973, 500257, 571743, 871335, 958265, 1511583, 1621273, 2449259, 3095511, 4335385, 4957877, 7554717, 8407537, 12325993, 14301411, 20348691, 22896077, 33647199, 40267141, 56412983, 66090291, 93371665, 106615841, 155161833

Offset

0,4

Links

Table of n, a(n) for n=0..60.

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(7) = 13 splits:
  (1)  (2)  (3)    (4)    (5)    (6)        (7)
            (1,2)  (1,3)  (1,4)  (1,5)      (1,6)
            (2,1)  (3,1)  (2,3)  (2,4)      (2,5)
                          (3,2)  (4,2)      (3,4)
                          (4,1)  (5,1)      (4,3)
                                 (1,2,3)    (5,2)
                                 (1,3,2)    (6,1)
                                 (2,1,3)    (1,2,4)
                                 (2,3,1)    (1,4,2)
                                 (3,1,2)    (2,1,4)
                                 (3,2,1)    (2,4,1)
                                 (1,2),(3)  (4,1,2)
                                 (2,1),(3)  (4,2,1)
                                 (3),(1,2)
                                 (3),(2,1)

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], SameQ@@Total/@#&]], {ctn, Join@@Permutations/@Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 0, 15}]

Crossrefs

The version with different instead of equal sums is A336128.

Starting with a non-strict composition gives A074854.

Starting with a partition gives A317715.

Starting with a strict partition gives A318683.

Set partitions with equal block-sums are A035470.

Partitions of partitions are A001970.

Partitions of compositions are A075900.

Compositions of compositions are A133494.

Compositions of partitions are A323583.

Cf. A006951, A063834, A271619, A279375, A305551, A317508, A318684, A326519, A336127, A336132, A336134, A336135.

Sequence in context: A183483 A218663 A095355 * A069834 A064038 A051684

Adjacent sequences: A336127 A336128 A336129 * A336131 A336132 A336133

Keyword

nonn

Author

Gus Wiseman, Jul 11 2020

Extensions

a(31)-a(60) from Max Alekseyev, Feb 14 2024

Status

approved