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

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, 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, 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

Offset: 1

Author

Mats Granvik, Gary W. Adamson and Roger L. Bagula, Jul 27 2008, Sep 21 2008

Keywords

• tabl
• sign

Comments

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.

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]

Examples

			Determinant of:
1
is equal to 1.
Determinant of:
1,1
-1,1
is equal to 2.
Determinant of:
1,1,1
-1,1,0
-1,0,1
is equal to 3.
Determinant of:
1,1,1,1
-1,1,0,0
-1,0,1,0
0,-1,0,1
is equal to 4.
Determinant of:
1,1,1,1,1
-1,1,0,0,0
-1,0,1,0,0
0,-1,0,1,0
-1,0,0,0,1
is equal to 5.
Determinant of:
1,1,1,1,1,1
-1,1,0,0,0,0
-1,0,1,0,0,0
0,-1,0,1,0,0
-1,0,0,0,1,0
1,-1,-1,0,0,1
is equal to 6.
Determinant of:
1,1,1,1,1,1,1
-1,1,0,0,0,0,0
-1,0,1,0,0,0,0
0,-1,0,1,0,0,0
-1,0,0,0,1,0,0
1,-1,-1,0,0,1,0
-1,0,0,0,0,0,1
is equal to 7.
		

Links

• Solve My Math, Matrix Calculator.
• E. W. Weisstein, Redheffer Matrix.
• Wikipedia, Moebius Function Matrix.

Crossrefs

Cf. A008683, A143104, A000027.

Cf. A054525. [From Mats Granvik, Sep 21 2008]

Programs

Excel

=if(mod(row();column())=0;lookup(row()/column();A000027;A008683);if(row()=1;1;0))