%I #6 Mar 30 2012 18:57:12

%S 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,

%T 28,12,26,44,56,61,57,50,34,15,32,52,68,78,79,73,60,40,17,37,63,83,94,

%U 101,98,87,70,47,20,42,72,96,113,124,126,118,104,82,54,24,48

%N 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.

%C 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.

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

%e Northwest corner:

%e 1....3....6....9...

%e 2....7...13...19...

%e 4...11...21...31...

%e 5...16...30...45...

%t r=GoldenRatio;

%t f[i_,j_]:=Sum[Floor[j*(i-1+r)/(k-1+r)],{k,1,1+r+j(i-1+r)}];

%t TableForm[Table[f[i,j],{i,1,10},{j,1,10}]] (* A182849 *)

%Y Cf. A182801, A182846.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Dec 08 2010