OFFSET
1,2
COMMENTS
Joint-rank arrays are defined in the first comment at A182801.
FORMULA
T(i,j)=SUM{floor(j*(i-1+r)/(k-1+r)): r=sqrt(2), k>=1} for i>=1, j>=1.
EXAMPLE
Northwest corner:
1....3....5....9...12...
2....7...13...19...26...
4...11...21...32...44...
6...17...30...46...61...
The numbers j*(i-1+sqrt(2)), approximately:
(for i=1) 1.41, 2.83, 4.24,...
(for i=2) 2.41, 4.83, 7.24,...
(for i=3) 3.41, 6.83, 10.24,...
Replacing each by its rank gives
1....3....5
2....7...13
4...ll...21
MATHEMATICA
r=Sqrt[2];
f[i_, j_]:=Sum[Floor[j*(i-1+r)/(k-1+r)], {k, 1, 1+r+j(i-1+r)}];
TableForm[Table[f[i, j], {i, 1, 10}, {j, 1, 10}]] (*A182846*)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Dec 08 2010
STATUS
approved