A182848 Joint-rank array of the numbers j*(i-1+r), where r=sqrt(5), i>=1, j>=1, by antidiagonals.

1, 4, 2, 8, 7, 3, 12, 14, 11, 5, 17, 22, 21, 16, 6, 24, 30, 33, 29, 20, 9, 28, 40, 45, 44, 38, 26, 10, 35, 51, 59, 61, 57, 47, 32, 13, 41, 60, 73, 80, 77, 69, 56, 37, 15, 49, 71, 88, 97, 101, 94, 84, 66, 43, 18, 55, 82, 103, 115, 124, 123, 113, 99, 76, 50, 19, 64

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....4....8...12...17...
2....7...14...22...30...
3...11...21...33...45...
5...16...29...44...61...
		

Crossrefs

Cf. A182801, A182846.

Programs

Mathematica

r=Sqrt[5];
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(5).