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

Author

Gus Wiseman, Jul 16 2020

Keywords

• nonn

Comments

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

Examples

			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)
		

Links

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

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.

Programs

Mathematica

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