A336132 Number of ways to split a strict integer partition of n into contiguous subsequences all having different sums.

1, 1, 1, 3, 3, 5, 8, 11, 14, 21, 30, 37, 51, 66, 86, 120, 146, 186, 243, 303, 378, 495, 601, 752, 927, 1150, 1395, 1741, 2114, 2571, 3134, 3788, 4541, 5527, 6583, 7917, 9511, 11319, 13448, 16040, 18996, 22455, 26589, 31317, 36844, 43518, 50917, 59655, 69933

Offset

0,4

Links

Table of n, a(n) for n=0..48.

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) = 14 splits:
  (1)  (2)  (3)      (4)      (5)      (6)          (7)
            (2,1)    (3,1)    (3,2)    (4,2)        (4,3)
            (2),(1)  (3),(1)  (4,1)    (5,1)        (5,2)
                              (3),(2)  (3,2,1)      (6,1)
                              (4),(1)  (4),(2)      (4,2,1)
                                       (5),(1)      (4),(3)
                                       (3,2),(1)    (5),(2)
                                       (3),(2),(1)  (6),(1)
                                                    (4),(2,1)
                                                    (4,2),(1)
                                                    (4),(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], UnsameQ@@Total/@#&]], {ctn, Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 0, 30}]

Crossrefs

The version with equal instead of different sums is A318683.

Starting with a composition gives A336127.

Starting with a strict composition gives A336128.

Starting with a partition gives A336131.

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, A317715, A323433, A336130, A336134, A336135.

Sequence in context: A285069 A262736 A318684 * A200737 A200741 A271970

Adjacent sequences: A336129 A336130 A336131 * A336133 A336134 A336135

Keyword

nonn

Author

Gus Wiseman, Jul 11 2020

Status

approved