A054527 Triangle read by rows: T(n,k) = Moebius mu(k) (n >= 1, 1 <= k <= n).

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

Offset: 1

Author

N. J. A. Sloane, Apr 09 2000

Keywords

• sign
• tabl

Comments

Row sums = Mertens sequence = A002321; right border = mu(n) = A008683. - Gary W. Adamson, Jan 17 2007

M * Q as infinite lower triangular matrices; M = (1; 1, 1; 1, 1, 1; ...); Q = mu(n) in the main diagonal and the rest zeros. - Gary W. Adamson, Jan 17 2007

Terms in rows of this table appears to be the values of the minors in the first expansion of the determinant of the Redheffer matrix. - Mats Granvik, Aug 24 2008

Examples

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

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Crossrefs

Cf. A008683, A002321, A054521.

Programs

Haskell

import Data.List (inits)
a054527 n k = a054527_tabl !! (n-1) !! (k-1)
a054527_row n = a054527_tabl !! (n-1)
a054527_tabl = tail $ inits a008683_list
-- Reinhard Zumkeller, Sep 03 2015

Mathematica

Table[#[[1 ;; n]], {n, Length[#]}] &@ Array[MoebiusMu, 12] // Flatten (* Michael De Vlieger, Feb 05 2022 *)

Extensions

Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar