OFFSET
0,4
COMMENTS
A composition of n is a finite sequence of positive integers with sum n. It is complete if it covers an initial interval of positive integers.
EXAMPLE
The a(0) = 1 through a(6) = 11 compositions (empty column not shown):
() (1) (1,2) (1,1,2) (1,2,2) (1,2,3)
(2,1) (1,2,1) (2,1,2) (1,3,2)
(2,1,1) (2,2,1) (2,1,3)
(1,1,2,1) (2,3,1)
(1,2,1,1) (3,1,2)
(3,2,1)
(1,2,1,2)
(1,2,2,1)
(2,1,1,2)
(2,1,2,1)
(1,1,2,1,1)
MATHEMATICA
normQ[m_]:=Or[m=={}, Union[m]==Range[Max[m]]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], normQ[#]&&normQ[Length/@Split[#]]&]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 21 2019
EXTENSIONS
a(21)-a(35) from Alois P. Heinz, Jul 06 2020
STATUS
approved