A140865 - OEIS

%I #13 Oct 20 2024 08:48:49

%S 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,

%T 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

%N 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).

%C 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.

%H E. W. Weisstein, <a href="http://mathworld.wolfram.com/RedhefferMatrix.html">Redheffer Matrix</a>.

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

%e Table begins:

%e   1, 1, 1, 1, 1, 1, ...

%e   1, 0, 0, 1, 0, 1, ...

%e   1, 0, 1, 0, 0, 1, ...

%e   1, 0, 0, 1, 1, 0, ...

%e   1, 0, 0, 0, 1, 0, ...

%e   1, 1, 0, 0, 0, 1, ...

%e where

%e   T(2,2) has been changed from 1 to 0.

%e   T(4,5) has been changed from 0 to 1.

%e   T(6,2) has been changed from 0 to 1.

%e Values of the first six determinants: 1,-1,-1,0,-1,1.

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

%Y Cf. A008683, A051731.

%K more,nonn,tabl

%O 1,1

%A _Mats Granvik_, Jul 20 2008