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

1,2

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.

Links

Table of n, a(n) for n=1..87.

Example

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, ...

Prog

(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)

Crossrefs

Cf. A126988, A153881, A156827.

Sequence in context: A347046 A300322 A144220 * A130296 A126705 A367849

Adjacent sequences: A156823 A156824 A156825 * A156827 A156828 A156829

Keyword

sign,tabl

Author

Mats Granvik, Feb 16 2009

Status

approved