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

%I A182846 #8 Mar 30 2012 18:57:12
%S A182846 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,
%T A182846 29,14,24,42,55,61,59,50,36,15,28,51,67,77,81,75,62,41,18,33,60,82,95,
%U A182846 102,100,90,72,49,22,38,69,93,113,125,128,120,106,84,56,25,43
%N A182846 Joint-rank array of the numbers j*(i-1+r), where r=sqrt(2), i>=1, j>=1, by antidiagonals.
%C A182846 Joint-rank arrays are defined in the first comment at A182801.
%F A182846 T(i,j)=SUM{floor(j*(i-1+r)/(k-1+r)): r=sqrt(2), k>=1} for i>=1, j>=1.
%e A182846 Northwest corner:
%e A182846 1....3....5....9...12...
%e A182846 2....7...13...19...26...
%e A182846 4...11...21...32...44...
%e A182846 6...17...30...46...61...
%e A182846 The numbers j*(i-1+sqrt(2)), approximately:
%e A182846 (for i=1)  1.41, 2.83, 4.24,...
%e A182846 (for i=2)  2.41, 4.83, 7.24,...
%e A182846 (for i=3)  3.41, 6.83, 10.24,...
%e A182846 Replacing each by its rank gives
%e A182846 1....3....5
%e A182846 2....7...13
%e A182846 4...ll...21
%t A182846 r=Sqrt[2];
%t A182846 f[i_,j_]:=Sum[Floor[j*(i-1+r)/(k-1+r)],{k,1,1+r+j(i-1+r)}];
%t A182846 TableForm[Table[f[i,j],{i,1,10},{j,1,10}]] (*A182846*)
%Y A182846 Cf. A182801, A182847-A182849.
%K A182846 nonn,tabl
%O A182846 1,2
%A A182846 _Clark Kimberling_, Dec 08 2010