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A143142
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Square array T(n,k) read by antidiagonals up. Mobius function interleaved with k-1 zeros in each column. Redheffer type matrix.
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3
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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
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OFFSET
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1,1
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COMMENTS
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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]
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LINKS
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Table of n, a(n) for n=1..120.
Solve My Math, Matrix Calculator.
E. W. Weisstein, Redheffer Matrix.
Wikipedia, Moebius Function Matrix.
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EXAMPLE
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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.
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PROG
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(Excel) =if(mod(row(); column())=0; lookup(row()/column(); A000027; A008683); if(row()=1; 1; 0))
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CROSSREFS
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Cf. A008683, A143104, A000027.
Cf. A054525. [From Mats Granvik, Sep 21 2008]
Sequence in context: A127247 A127244 A144778 * A174856 A175608 A285467
Adjacent sequences: A143139 A143140 A143141 * A143143 A143144 A143145
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KEYWORD
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tabl,sign
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AUTHOR
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Mats Granvik, Gary W. Adamson and Roger L. Bagula, Jul 27 2008, Sep 21 2008
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STATUS
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approved
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