A156826 Square array read by antidiagonals up: same as A126988 except that the first row is A153881.

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, -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, 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

Offset: 1

Author

Mats Granvik, Feb 16 2009

Keywords

• sign
• tabl

Comments

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.

Examples

			Table begins:
   1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, ...
   2,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, ...
   3,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, ...
   4,  2,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0, ...
   5,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0, ...
   6,  3,  2,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0, ...
   7,  0,  0,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0, ...
   8,  4,  0,  2,  0,  0,  0,  1,  0,  0,  0,  0,  0, ...
   9,  0,  3,  0,  0,  0,  0,  0,  1,  0,  0,  0,  0, ...
  10,  5,  0,  0,  2,  0,  0,  0,  0,  1,  0,  0,  0, ...
  11,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  0,  0, ...
  12,  6,  4,  3,  0,  2,  0,  0,  0,  0,  0,  1,  0, ...
  13,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1, ...
		

Crossrefs

Cf. A126988, A153881, A156827.

Programs

Excel

=rounddown(if(mod(row();column())=0;row()/column();-row()/column())*if(row()=1;column();1);0)

Excel

with fractions: =if(mod(row();column())=0;row()/column();-row()/column())*if(row()=1;column();1)