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%I #10 Dec 10 2016 10:32:01
%S 1,2,-1,3,1,-1,4,-1,0,-1,5,2,1,0,-1,6,-2,-1,0,0,-1,7,3,-1,1,0,0,-1,8,
%T -3,2,-1,0,0,0,-1,9,4,-2,-1,1,0,0,0,-1,10,-4,-2,-1,-1,0,0,0,0,-1,11,5,
%U 3,2,-1,1,0,0,0,0,-1,12,-5,-3,-2,-1,-1,0,0,0,0,0,-1,13,6,-3,-2,-1,-1,1,0,0
%N Square array read by antidiagonals up: same as A126988 except that the first row is A153881.
%C Replace the zeros with -n/k. That is, the fraction of the row index divided by the column index with a negative sign. Then swap the element in the lower right corner with the element in the upper right corner and calculate the determinant. The result appears to be sequence A156827.
%e Table begins:
%e 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, ...
%e 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 4, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 5, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 6, 3, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, ...
%e 7, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, ...
%e 8, 4, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, ...
%e 9, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, ...
%e 10, 5, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, ...
%e 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, ...
%e 12, 6, 4, 3, 0, 2, 0, 0, 0, 0, 0, 1, 0, ...
%e 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, ...
%o (Excel) =rounddown(if(mod(row();column())=0;row()/column();-row()/column())*if(row()=1;column();1);0)
%o (Excel) with fractions: =if(mod(row();column())=0;row()/column();-row()/column())*if(row()=1;column();1)
%Y Cf. A126988, A153881, A156827.
%K sign,tabl
%O 1,2
%A _Mats Granvik_, Feb 16 2009
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