A124755 Binomial sum of compositions in standard order.

0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 4, 6, 5, 8, 5, 5, 5, 6, 5, 7, 6, 9, 5, 8, 7, 11, 6, 11, 9, 16, 6, 6, 6, 7, 6, 8, 7, 10, 6, 9, 8, 12, 7, 12, 10, 17, 6, 10, 9, 14, 8, 14, 12, 20, 7, 14, 12, 22, 10, 20, 17, 32, 7, 7, 7, 8, 7, 9, 8, 11, 7, 10, 9, 13, 8, 13, 11, 18, 7, 11, 10, 15, 9, 15, 13, 21, 8, 15

Offset

0,3

Comments

The standard order of compositions is given by A066099.

This is the final term of the binomial transform of the composition.

Links

Alois P. Heinz, Rows n = 0..14, flattened

Formula

For a composition b(1),...,b(k), a(n) = Sum_{i=1}^k C(k-1,i-1) b(i).

Example

Composition number 11 is 2,1,1; 1*2+2*1+1*1 = 5, so a(11) = 5.
The table starts:
0
1
2 2
3 3 3 4

Crossrefs

Cf. A066099, A070939, A124756, A011782 (row lengths), A003462 (row sums).

Sequence in context: A194295 A194287 A194303 * A354586 A364480 A033810

Adjacent sequences: A124752 A124753 A124754 * A124756 A124757 A124758

Keyword

easy,nonn,tabf

Author

Franklin T. Adams-Watters, Nov 06 2006

Status

approved