... <t<√3,itholdsthatα(t)√3+t=α(−t)√3−t.(Theorem 1. 1 is easily and directly verified when t =±√3/3, since the rate of growth of the sequence of every other Fibonacci number is the square of the rate of growth of the Fibonacci sequence.) Generalized ... the sequence of every other Fibonacci number F0,F2,F4, , as illustr ated in Figure 1. 1;forafixedt, the sequence{ᏸk(t)}∞k=0is called the generalized Fibonacci sequence induced by the ... NUMBERS DONNIELL E. FISHKIND Received 1 May 2004 Let α(t) be the limiting ratio of the generalized Fibonacci numbers produced by sum-ming along lines of slope t through the natural arrayal of Pascal’s...