A124754 Alternating sum of compositions in standard order.

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

Offset: 0

Author

Franklin T. Adams-Watters, Nov 06 2006

Keywords

• easy
• sign
• tabf

Comments

The standard order of compositions is given by A066099.

The sum of row n is 2^{n-1} for n>0.

Examples

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

Links

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

Crossrefs

Cf. A066099, A070939, A124756, A011782 (row lengths), A106400.

Formula

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

a(2^k) = k+1. If n = 2^e_1 + 2^e_2 + k, 0 <= k < 2^e_2 < 2^e_1, then a(n) = (e_1 - e_2) - a(2^e_2 + k).

a(0) = 0; for n>0, a(n) = a(floor(n/2)) - A106400(n).