A128407 Triangle read by rows: T(n,n) = mobius(n) on the diagonal, zero elsewhere.

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

Offset

1,1

Comments

A128407 * [1,2,3,...] = n*mu(n), A055615: (1, -2, -3, 0, -5, 6, -7, 0, ...). A051731 * A128407 = A054524. A128407 * A051731 = A128408.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

Infinite lower triangular matrix with mu(n), A008683, as the right border and the rest zeros.

Example

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

Mathematica

Table[PadLeft[{MoebiusMu[n]}, n], {n, 10}]//Flatten (* Harvey P. Dale, Dec 29 2021 *)

Crossrefs

Cf. A051731, A128408, A008683 (row sums and diagonal), A054524.

Sequence in context: A074381 A179560 A341602 * A363800 A134286 A023531

Adjacent sequences: A128404 A128405 A128406 * A128408 A128409 A128410

Keyword

tabl,sign,easy

Author

Gary W. Adamson, Mar 01 2007

Extensions

Name improved . - R. J. Mathar, Aug 03 2015

Status

approved