A156826 - OEIS

%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