A140865 Square array read by upward antidiagonals. Modified Redheffer matrix for which the first 6 values of A008683 are given as determinants of T(n,k).

1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1

Offset

1,1

Comments

It seems to be possible to modify the Redheffer matrix in several ways in order to calculate the Mobius function as determinants. However, the modifications don't seem to follow any clear pattern.

Links

Table of n, a(n) for n=1..66.

E. W. Weisstein, Redheffer Matrix.

Formula

T(n,k) = 1 if k=1 or k mod n = 0, otherwise 0. Produces the Redheffer matrix, changes as in example below.

Example

Table begins:
  1, 1, 1, 1, 1, 1, ...
  1, 0, 0, 1, 0, 1, ...
  1, 0, 1, 0, 0, 1, ...
  1, 0, 0, 1, 1, 0, ...
  1, 0, 0, 0, 1, 0, ...
  1, 1, 0, 0, 0, 1, ...
where
  T(2,2) has been changed from 1 to 0.
  T(4,5) has been changed from 0 to 1.
  T(6,2) has been changed from 0 to 1.
Values of the first six determinants: 1,-1,-1,0,-1,1.

Prog

(Excel) =if(mod(column(); row())=0; 1; if(column()=1; 1; 0)). Produces the Redheffer matrix.

Crossrefs

Cf. A008683, A051731.

Sequence in context: A127970 A158856 A154957 * A114000 A131218 A174391

Adjacent sequences: A140862 A140863 A140864 * A140866 A140867 A140868

Keyword

more,nonn,tabl

Author

Mats Granvik, Jul 20 2008

Status

approved