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

Author

Gary W. Adamson, Mar 01 2007

Keywords

• tabl
• sign
• easy

Comments

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

Examples

			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;
  ...
		

Links

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

Crossrefs

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

Programs

Mathematica

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

Formula

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

Extensions

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