A143353 Triangle read by rows, A127172 * A128407 = (A051731)^3 * A128407, 1<=k<=n.

1, 3, -1, 3, 0, -1, 6, -3, 0, 0, 3, 0, 0, 0, -1, 9, -3, -3, 0, 0, 1, 3, 0, 0, 0, 0, 0, -1, 10, -6, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 9, -3, 0, 0, -3, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 18, -9, -6, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 9, -3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Gary W. Adamson, Aug 10 2008

Keywords

• tabl
• sign

Comments

Left border = A007425.

Right border = mu(n), A008683.

Row sums = d(n), A000010: (1, 2, 2, 3, 2, 4, 2,...).

Examples

			First few rows of the triangle =
1;
3, -1;
3, 0, -1;
6, -3, 0, 0;
3, 0, 0, 0, -1;
9, -3, -3, 0, 0, 1;
3, 0, 0, 0, 0, 0, -1;
10, -6, 0, 0, 0, 0, 0, 0;
6, 0, -3, 0, 0, 0, 0, 0, 0;
9, -3, 0, 0, -3, 0, 0, 0, 0, 1;
...
		

Crossrefs

Cf. A007425, A127172, A128407, A051731, A000010, A008683.

Formula

Triangle read by rows, A127172 * A128407 = (A051731)^3 * A128407, 1<=k<=n