%I #4 Mar 30 2012 18:57:05

%S 1,2,1,3,3,1,5,4,4,1,8,7,5,5,1,13,11,9,6,6,2,21,18,14,11,7,5,1,34,29,

%T 23,17,13,7,7,1,55,47,37,28,20,12,8,8,2,89,76,60,45,33,19,15,9,7,1,

%U 144,123,97,73,53,31,23,17,9,9,3,233,199,157,118,86,50,38,26,16,10,7,1,377,322

%N Rectangular array T(n,k) by antidiagonals; rows are generalized Fibonacci sequences and every relatively prime pair (i,j) satisfying 1 <= i < j occurs exactly once.

%C In every row, the limiting ratio of consecutive terms is tau.

%F Recurrence for row n: T(n, k)=T(n, k-1)+T(n, k-2). Each row after the first begins with lexically least relatively prime pair not in previous rows.

%e Northwest corner:

%e 1 2 3 5 8

%e 1 3 4 7 11

%e 1 4 5 9 14

%e 1 5 6 11 17

%e 1 6 7 13 20

%e 2 5 7 12 19

%Y Cf. A000045, A097352.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Aug 08 2004