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A143142 Square array T(n,k) read by antidiagonals up. Mobius function interleaved with k-1 zeros in each column. Redheffer type matrix.

%I A143142 #6 Feb 16 2025 08:33:08
%S A143142 1,-1,1,-1,1,1,0,0,0,1,-1,-1,1,0,1,1,0,0,0,0,1,-1,-1,0,1,0,0,1,0,0,-1,
%T A143142 0,0,0,0,1,0,0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,-1,-1,-1,-1,0,1,0,0,
%U A143142 0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,-1,0,0,0,0,0,0,0,0,1,1,-1,0,-1,0,0,0,1,0,0,0,0,0,0,1
%N A143142 Square array T(n,k) read by antidiagonals up. Mobius function interleaved with k-1 zeros in each column. Redheffer type matrix.
%C A143142 Determinant of the n times n matrix with T(n,n)=0 is equal to 1 for every such matrix. Tested up to n=13.
%C A143142 For elements where row index is greater than column index, every negative number appears to give a positive contribution while every positive number appears to give a negative contribution to the determinant of the matrix. The size of a such contribution appears to be 1 when replacing the number with a zero. [From _Mats Granvik_, Sep 22 2008]
%H A143142 Solve My Math, <a href="http://www.solvemymath.com/online_math_calculator/algebra_combinatorics/matrix/index.php">Matrix Calculator</a>.
%H A143142 E. W. Weisstein, <a href="https://mathworld.wolfram.com/RedhefferMatrix.html">Redheffer Matrix</a>.
%H A143142 Wikipedia, <a href="http://en.wikipedia.org/wiki/M%C3%B6bius_function">Moebius Function Matrix</a>.
%e A143142 Determinant of:
%e A143142 1
%e A143142 is equal to 1.
%e A143142 Determinant of:
%e A143142 1,1
%e A143142 -1,1
%e A143142 is equal to 2.
%e A143142 Determinant of:
%e A143142 1,1,1
%e A143142 -1,1,0
%e A143142 -1,0,1
%e A143142 is equal to 3.
%e A143142 Determinant of:
%e A143142 1,1,1,1
%e A143142 -1,1,0,0
%e A143142 -1,0,1,0
%e A143142 0,-1,0,1
%e A143142 is equal to 4.
%e A143142 Determinant of:
%e A143142 1,1,1,1,1
%e A143142 -1,1,0,0,0
%e A143142 -1,0,1,0,0
%e A143142 0,-1,0,1,0
%e A143142 -1,0,0,0,1
%e A143142 is equal to 5.
%e A143142 Determinant of:
%e A143142 1,1,1,1,1,1
%e A143142 -1,1,0,0,0,0
%e A143142 -1,0,1,0,0,0
%e A143142 0,-1,0,1,0,0
%e A143142 -1,0,0,0,1,0
%e A143142 1,-1,-1,0,0,1
%e A143142 is equal to 6.
%e A143142 Determinant of:
%e A143142 1,1,1,1,1,1,1
%e A143142 -1,1,0,0,0,0,0
%e A143142 -1,0,1,0,0,0,0
%e A143142 0,-1,0,1,0,0,0
%e A143142 -1,0,0,0,1,0,0
%e A143142 1,-1,-1,0,0,1,0
%e A143142 -1,0,0,0,0,0,1
%e A143142 is equal to 7.
%o A143142 (Excel) =if(mod(row();column())=0;lookup(row()/column();A000027;A008683);if(row()=1;1;0))
%Y A143142 Cf. A008683, A143104, A000027.
%Y A143142 Cf. A054525. [From _Mats Granvik_, Sep 21 2008]
%K A143142 tabl,sign
%O A143142 1,1
%A A143142 _Mats Granvik_, _Gary W. Adamson_ and _Roger L. Bagula_, Jul 27 2008, Sep 21 2008