A143442 Triangle read by rows, A127648 * A000012 * A128407, 1 <= k <= n.

1, 2, -2, 3, -3, -3, 4, -4, -4, 0, 5, -5, -5, 0, -5, 6, -6, -6, 0, -6, 6, 7, -7, -7, 0, -7, 7, -7, 8, -8, -8, 0, -8, 8, -8, 0, 9, -9, -9, 0, -9, 9, -9, 0, 0, 10, -10, -10, 0, -10, 10, -10, 0, 0, 10, 11, -11, -11, 0, -11, 11, -11, 0, 0, 11, -11

Offset: 1

Author

Gary W. Adamson, Aug 15 2008

Keywords

• tabl
• sign

Comments

Row sums = A143443, n * (A002321, the Mertens function) = (1, 0, -3, -4, -10, -6, ...).

Right border = n*mu(n).

Examples

			First few rows of the triangle =
1;
2, -2;
3, -3, -3;
4, -4, -4, 0;
5, -5, -5, 0, -5;
6, -6, -6, 0, -6, 6;
7, -7, -7, 0, -7, 7, -7;
...
		

Crossrefs

Cf. A002321, A008683, A127648, A128407, A143443.

Formula

Triangle read by rows, A127648 * A000012 * A128407, 1 <= k <= n; where A127648 = an infinite lower triangular matrix with (1, 2, 3, ...) in the main diagonal, the rest zeros. A128407 = diagonalized mu(n) matrix.