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

%I A054527 #16 Feb 06 2022 10:08:17
%S A054527 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 A054527 -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 A054527 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 A054527 Triangle read by rows: T(n,k) = Moebius mu(k) (n >= 1, 1 <= k <= n).
%C A054527 Row sums = Mertens sequence = A002321; right border = mu(n) = A008683. - _Gary W. Adamson_, Jan 17 2007
%C A054527 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 A054527 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 A054527 Reinhard Zumkeller, <a href="/A054527/b054527.txt">Rows n = 1..125 of triangle, flattened</a>
%e A054527 First few rows of the triangle:
%e A054527   1;
%e A054527   1, -1;
%e A054527   1, -1, -1;
%e A054527   1, -1, -1,  0;
%e A054527   1, -1, -1,  0, -1;
%e A054527   1, -1, -1,  0, -1,  1;
%e A054527   ...
%t A054527 Table[#[[1 ;; n]], {n, Length[#]}] &@ Array[MoebiusMu, 12] // Flatten (* _Michael De Vlieger_, Feb 05 2022 *)
%o A054527 (Haskell)
%o A054527 import Data.List (inits)
%o A054527 a054527 n k = a054527_tabl !! (n-1) !! (k-1)
%o A054527 a054527_row n = a054527_tabl !! (n-1)
%o A054527 a054527_tabl = tail $ inits a008683_list
%o A054527 -- _Reinhard Zumkeller_, Sep 03 2015
%Y A054527 Cf. A008683, A002321, A054521.
%K A054527 sign,tabl
%O A054527 1,1
%A A054527 _N. J. A. Sloane_, Apr 09 2000
%E A054527 Edited by _N. J. A. Sloane_, Jul 03 2008 at the suggestion of _R. J. Mathar_