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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. 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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

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Last modified December 2 07:25 EST 2020. Contains 338868 sequences. (Running on oeis4.)