%I #3 Apr 25 2016 11:45:53
%S -1,1,1,1,-1,1,0,0,0,0,1,1,-1,1,1,-1,0,0,0,0,-1,1,1,0,-1,0,1,1,0,0,1,
%T 0,0,1,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,1,1,1,1,0,-1,0,1,
%U 1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,-1,0,0,0,0,-1,1,-1,0,0,0,1,0
%N Square array read by upwards antidiagonals.
%C Partial sums + 2 are the natural numbers. For rows greater than columns the mobius function times -1 is interleaved with column-1 zeros in the columns. For columns greater than rows the mobius function times -1 is interleaved with row-1 zeros in the rows.
%e Table begins;
%e -1..1..1..0..1.-1..1..0
%e .1.-1..0..1..0..1..0..0
%e .1..0.-1..0..0..1..0..0
%e .0..1..0.-1..0..0..0..1
%e .1..0..0..0.-1..0..0..0
%e -1..1..1.,0..0.-1..0..0
%e .1..0..0..0..0..0.-1..0
%e .0..0..0..1..0..0..0.-1
%e and partial sums + 2 are: 1,2,3,4,5,6,7,8,9...
%o (Excel) =if(mod(row();column())=0;-1*lookup(row()/column();A000027;A008683);if(mod(column();row())=0;-1*lookup(column()/row();A000027;A008683);0))
%Y Cf. A000027, A008683.
%K sign,tabl
%O 1,1
%A _Mats Granvik_, Dec 09 2008