|
| |
|
|
A124755
|
|
Binomial sum of compositions in standard order.
|
|
1
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
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.
|
|
|
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 * A033810 A023965 A087847
Adjacent sequences: A124752 A124753 A124754 * A124756 A124757 A124758
|
|
|
KEYWORD
| easy,nonn,tabf
|
|
|
AUTHOR
| Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 06 2006
|
| |
|
|
