A124756 Inverse binomial sum of compositions in standard order.

0, 1, 2, 0, 3, 1, -1, 0, 4, 2, 0, 1, -2, -2, 1, 0, 5, 3, 1, 2, -1, -1, 2, 1, -3, -4, -1, -3, 2, 3, -1, 0, 6, 4, 2, 3, 0, 0, 3, 2, -2, -3, 0, -2, 3, 4, 0, 1, -4, -6, -3, -6, 0, 0, -4, -4, 3, 6, 2, 6, -2, -4, 1, 0, 7, 5, 3, 4, 1, 1, 4, 3, -1, -2, 1, -1, 4, 5, 1, 2, -3, -5, -2, -5, 1, 1, -3, -3, 4, 7, 3, 7, -1, -3, 2, 1, -5, -8, -5, -9, -2

Offset

0,3

Comments

The standard order of compositions is given by A066099.

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

Links

Table of n, a(n) for n=0..100.

Formula

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

Example

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

Crossrefs

Cf. A066099, A124754, A124755, A011782 (row lengths), A001477 (row sums).

Sequence in context: A325660 A342657 A002187 * A113504 A358726 A357623

Adjacent sequences: A124753 A124754 A124755 * A124757 A124758 A124759

Keyword

easy,sign,tabf

Author

Franklin T. Adams-Watters, Nov 06 2006

Status

approved