A176918 Triangle read by rows, a signed variant of A077049 * A128407; as infinite lower triangular matrices.

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

Offset: 1

Author

Gary W. Adamson and Mats Granvik, Apr 29 2010

Keywords

• tabl
• sign

Comments

Row sums = mu(n), A008683

Examples

			First few rows of triangle A176918 =
1;
-1, 0;
-1, 0, 0;
-1, 1, 0, 0;
-1, 0, 0, 0, 0;
-1, 1, 1, 0, 0, 0;
-1, 0, 0, 0, 0, 0, 0;
-1, 1, 0, 0, 0, 0, 0, 0;
-1, 0, 1, 0, 0, 0, 0, 0, 0;
-1, 1, 0, 0, 1, 0, 0, 0, 0, 0;
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
-1, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0;
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
-1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
-1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
-1, 1, 1, 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, 0, 0, 0, 0, 0, 0, 0;
-1, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
-1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
-1, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
-1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
...
		

Crossrefs

Cf. A077049, A128407, A008683, A176890 (another version).

Formula

Given (-1)*triangle A077049, preface this with a "1" as row 1; = M.

Perform M * A128407 (the diagonalized variant of A008683); = A176918 as an

infinite lower triangular matrix.