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A156826
Square array read by antidiagonals up: same as A126988 except that the first row is A153881.
1
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.
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
KEYWORD
sign,tabl
AUTHOR
Mats Granvik, Feb 16 2009
STATUS
approved