A054527 - OEIS

%I #16 Feb 06 2022 10:08:17

%S 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,

%T -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,

%U 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

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

%C Row sums = Mertens sequence = A002321; right border = mu(n) = A008683. - _Gary W. Adamson_, Jan 17 2007

%C 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

%C 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

%H Reinhard Zumkeller, <a href="/A054527/b054527.txt">Rows n = 1..125 of triangle, flattened</a>

%e First few rows of the triangle:

%e   1;

%e   1, -1;

%e   1, -1, -1;

%e   1, -1, -1,  0;

%e   1, -1, -1,  0, -1;

%e   1, -1, -1,  0, -1,  1;

%e   ...

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

%o (Haskell)

%o import Data.List (inits)

%o a054527 n k = a054527_tabl !! (n-1) !! (k-1)

%o a054527_row n = a054527_tabl !! (n-1)

%o a054527_tabl = tail $ inits a008683_list

%o -- _Reinhard Zumkeller_, Sep 03 2015

%Y Cf. A008683, A002321, A054521.

%K sign,tabl

%O 1,1

%A _N. J. A. Sloane_, Apr 09 2000

%E Edited by _N. J. A. Sloane_, Jul 03 2008 at the suggestion of _R. J. Mathar_