OFFSET
0,4
COMMENTS
The standard order of compositions is given by A066099.
The k-th term of the composition is the number of objects with rank k. The rank of an object is one more than the maximum rank of any smaller object in the ordering (1 for a minimal element), or equivalently the size of the largest chain of which the object is the maximal element.
EXAMPLE
Composition number 11 is 2,1,1; there are 3 partial orders
associated with this (shown below); these can be labeled respectively
in 12, 24 and 24 ways, so a(11) = 12+24+24 = 60.
..O..*O..*..O
..|..*|..*./|
..O..*O..*O.|
./.\.*|..*|.|
O...O*O.O*O.O
The table starts:
1
1
1 2
1 9 3 6
CROSSREFS
KEYWORD
more,nonn,tabf
AUTHOR
Franklin T. Adams-Watters, Nov 06 2006
STATUS
approved