A124777 Number of naturally labeled partially ordered sets associated with compositions in standard order.

1, 1, 1, 1, 1, 4, 1, 1, 1, 11, 13, 8, 1, 4, 1, 1

Offset

0,6

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.

Links

Table of n, a(n) for n=0..15.

Example

Composition number 11 is 2,1,1; there are 3 partial orders
associated with this (shown below); these can be naturally labeled
respectively in 1, 4 and 3 ways, so a(11) = 1+4+3 = 8.
..O..*O..*..O
..|..*|..*./|
..O..*O..*O.|
./.\.*|..*|.|
O...O*O.O*O.O
The table starts:
1
1
1 1
1 4 1 1

Crossrefs

Cf. A066099, A124775, A124776, A011782 (row lengths), A006455 (row sums).

Sequence in context: A037291 A222317 A063851 * A352834 A203639 A358319

Adjacent sequences: A124774 A124775 A124776 * A124778 A124779 A124780

Keyword

more,nonn,tabf

Author

Franklin T. Adams-Watters, Nov 06 2006

Status

approved