A182846 Joint-rank array of the numbers j*(i-1+r), where r=sqrt(2), i>=1, j>=1, by antidiagonals.

1, 3, 2, 5, 7, 4, 9, 13, 11, 6, 12, 19, 21, 17, 8, 16, 26, 32, 30, 23, 10, 20, 35, 44, 46, 39, 29, 14, 24, 42, 55, 61, 59, 50, 36, 15, 28, 51, 67, 77, 81, 75, 62, 41, 18, 33, 60, 82, 95, 102, 100, 90, 72, 49, 22, 38, 69, 93, 113, 125, 128, 120, 106, 84, 56, 25, 43

Offset: 1

Author

Clark Kimberling, Dec 08 2010

Keywords

• nonn
• tabl

Comments

Joint-rank arrays are defined in the first comment at A182801.

Examples

			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
		

Crossrefs

Cf. A182801, A182847-A182849.

Programs

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*)

Formula

T(i,j)=SUM{floor(j*(i-1+r)/(k-1+r)): r=sqrt(2), k>=1} for i>=1, j>=1.