

A143142


Square array T(n,k) read by antidiagonals up. Mobius function interleaved with k1 zeros in each column. Redheffer type matrix.


3



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

1,1


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]


LINKS

Table of n, a(n) for n=1..120.
Solve My Math, Matrix Calculator.
E. W. Weisstein, Redheffer Matrix.
Wikipedia, Moebius Function Matrix.


EXAMPLE

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.


PROG

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


CROSSREFS

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


KEYWORD

tabl,sign


AUTHOR

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


STATUS

approved



