

A124755


Binomial sum of compositions in standard order.


2



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;
text;
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.


LINKS

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


FORMULA

For a composition b(1),...,b(k), a(n) = Sum_{i=1}^k C(k1,i1) 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 A253272 A023965
Adjacent sequences: A124752 A124753 A124754 * A124756 A124757 A124758


KEYWORD

easy,nonn,tabf


AUTHOR

Franklin T. AdamsWatters, Nov 06 2006


STATUS

approved



