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

Author

Gus Wiseman, Jul 11 2020

Keywords

• nonn

Examples

			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)
		

Links

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

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.

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

Extensions

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