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A054527 Triangle read by rows: T(n,k) = Moebius mu(k) (n >= 1, 1<=k<=n). 2

%I

%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. [From _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 are;

%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 ...

%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

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Last modified November 15 21:37 EST 2019. Contains 329168 sequences. (Running on oeis4.)