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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, 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.
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
Sequence in context: A127970 A158856 A154957 * A114000 A131218 A174391
KEYWORD
more,nonn,tabl
AUTHOR
Mats Granvik, Jul 20 2008
STATUS
approved