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

1,1

Comments

Row sums = mu(n), A008683

Links

Table of n, a(n) for n=1..74.

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.

Example

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).

Sequence in context: A318963 A350600 A295896 * A176890 A164057 A140820

Adjacent sequences: A176915 A176916 A176917 * A176919 A176920 A176921

Keyword

tabl,sign

Author

Gary W. Adamson and Mats Granvik, Apr 29 2010

Status

approved