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

1,1

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

Links

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

Example

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;
  ...

Mathematica

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

Prog

(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

Crossrefs

Cf. A008683, A002321, A054521.

Sequence in context: A279693 A368992 A334465 * A137794 A357731 A336546

Adjacent sequences: A054524 A054525 A054526 * A054528 A054529 A054530

Keyword

sign,tabl

Author

N. J. A. Sloane, Apr 09 2000

Extensions

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

Status

approved