A182847 Joint-rank array of the numbers j*(i-1+r), where r=sqrt(3), i>=1, j>=1, by diagonals.

1, 3, 2, 6, 7, 4, 10, 13, 11, 5, 14, 20, 21, 16, 8, 18, 27, 32, 30, 22, 9, 24, 36, 42, 44, 38, 26, 12, 29, 46, 55, 61, 58, 49, 33, 15, 34, 54, 69, 77, 78, 72, 59, 40, 17, 39, 64, 84, 95, 100, 98, 87, 70, 47, 19, 45, 73, 97, 113, 123, 124, 117, 103, 80

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....6...10...
2....7...13...20...
4...11...21...32...
5...16...30...44...
		

Crossrefs

Cf. A182801, A182846, A182848, A182849.

Programs

Mathematica

r=Sqrt[3];
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}]]

Formula

T(i,j)=sum(k>=1, floor( j*(i-1+r)/(k-1+r) ) ) where r=sqrt(3), for i>=1, j>=1.