A128408 Triangle read by rows: A128407 * A051731 as infinite lower triangular matrices.

1, -1, -1, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 1, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Gary W. Adamson, Mar 01 2007

Keywords

• tabl
• sign

Comments

Left and right borders = mu(n), A008683. Row sums = A008966: (1, -2, -2, 0, -2, 4, -2, 0, 0, 4, ...). A128408 * [1,2,3,...] = A063441: (1, -3, -4, 0, -6, 12, ...). A054524 = A051731 * A128407.

Examples

			First few rows of the triangle:
   1;
  -1, -1;
  -1,  0, -1;
   0,  0,  0,  0;
  -1,  0,  0,  0, -1;
   1,  1,  1,  0,  0,  1;
  ...
		

Crossrefs

Cf. A008683, A008966, A054524, A063441, A128407.

Extensions

a(45) = 0 inserted and more terms from Georg Fischer, Jun 05 2023