A336139 Number of ways to choose a strict composition of each part of a strict composition of n.

1, 1, 1, 5, 9, 17, 45, 81, 181, 397, 965, 1729, 3673, 7313, 15401, 34065, 68617, 135069, 266701, 556969, 1061921, 2434385, 4436157, 9120869, 17811665, 35651301, 68949549, 136796317, 283612973, 537616261, 1039994921, 2081261717, 3980842425, 7723253181, 15027216049

Offset

0,4

Comments

A strict composition of n is a finite sequence of distinct positive integers summing to n.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Example

The a(1) = 1 through a(5) = 17 splittings:
  (1)  (2)  (3)      (4)        (5)
            (1,2)    (1,3)      (1,4)
            (2,1)    (3,1)      (2,3)
            (1),(2)  (1),(3)    (3,2)
            (2),(1)  (3),(1)    (4,1)
                     (1),(1,2)  (1),(4)
                     (1),(2,1)  (2),(3)
                     (1,2),(1)  (3),(2)
                     (2,1),(1)  (4),(1)
                                (1),(1,3)
                                (1,2),(2)
                                (1),(3,1)
                                (1,3),(1)
                                (2),(1,2)
                                (2,1),(2)
                                (2),(2,1)
                                (3,1),(1)

Mathematica

strs[n_]:=Join@@Permutations/@Select[IntegerPartitions[n], UnsameQ@@#&];
Table[Length[Join@@Table[Tuples[strs/@ctn], {ctn, strs[n]}]], {n, 0, 15}]

Crossrefs

The version for partitions is A063834.

Row sums of A072574.

The version for non-strict compositions is A133494.

The version for strict partitions is A279785.

Multiset partitions of partitions are A001970.

Strict compositions are A032020.

Taking a composition of each part of a partition: A075900.

Taking a composition of each part of a strict partition: A304961.

Taking a strict composition of each part of a composition: A307068.

Splittings of partitions are A323583.

Compositions of parts of strict compositions are A336127.

Set partitions of strict compositions are A336140.

Cf. A318683, A318684, A319794, A336128, A336130, A336132.

Sequence in context: A324718 A099213 A146067 * A295627 A300128 A334993

Adjacent sequences: A336136 A336137 A336138 * A336140 A336141 A336142

Keyword

nonn

Author

Gus Wiseman, Jul 16 2020

Status

approved