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

%I #8 Mar 30 2012 18:57:12

%S 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,

%T 26,12,29,46,55,61,58,49,33,15,34,54,69,77,78,72,59,40,17,39,64,84,95,

%U 100,98,87,70,47,19,45,73,97,113,123,124,117,103,80

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

%C Joint-rank arrays are defined in the first comment at A182801.

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

%e Northwest corner:

%e 1....3....6...10...

%e 2....7...13...20...

%e 4...11...21...32...

%e 5...16...30...44...

%t r=Sqrt[3];

%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}]]

%Y Cf. A182801, A182846, A182848, A182849.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Dec 08 2010