A143352 Triangle read by rows, A051731 * A054524 = (A051731)^2 * A128407; 1<=k<=n.

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

Offset: 1

Author

Gary W. Adamson, Aug 10 2008

Keywords

• tabl
• sign

Comments

Left border = d(n), A000010.

Right border = mu(n), A008683.

Row sums = 1.

Examples

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

Crossrefs

Cf. A054524, A051731, A128407, A000010, A008683.

Formula

Triangle read by rows, A051731 * A054524 = (A051731)^2 * A128407; 1<=k<=n