A182849 Joint-rank array of the numbers j*(i-1+r), where r = golden ratio = (1+sqrt(5))/2, and i>=1, j>=1, by antidiagonals.

1, 3, 2, 6, 7, 4, 9, 13, 11, 5, 14, 19, 21, 16, 8, 18, 27, 31, 30, 22, 10, 23, 36, 43, 45, 39, 28, 12, 26, 44, 56, 61, 57, 50, 34, 15, 32, 52, 68, 78, 79, 73, 60, 40, 17, 37, 63, 83, 94, 101, 98, 87, 70, 47, 20, 42, 72, 96, 113, 124, 126, 118, 104, 82, 54, 24, 48

Offset

1,2

Comments

Joint-rank arrays are defined in the first comment at A182801. Every positive integer occurs exactly once, so that as a sequence, A182849 is a permutation of the positive integers.

Links

Table of n, a(n) for n=1..67.

Formula

T(i,j)=SUM{floor(j*(i-1+r)/(k-1+r)): r=(1+sqrt(5))/2, k>=1} for i>=1, j>=1.

Example

Northwest corner:
1....3....6....9...
2....7...13...19...
4...11...21...31...
5...16...30...45...

Mathematica

r=GoldenRatio;
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}]] (* A182849 *)

Crossrefs

Cf. A182801, A182846.

Sequence in context: A268825 A245812 A268826 * A120231 A083362 A182847

Adjacent sequences: A182846 A182847 A182848 * A182850 A182851 A182852

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 08 2010

Status

approved