ON THE GROWTH RATE OF GENERALIZED FIBONACCI NUMBERS DONNIELL E. FISHKIND Received 1 May 2004 Let

ON THE GROWTH RATE OF GENERALIZED FIBONACCI NUMBERS DONNIELL E. FISHKIND Received 1 May 2004 Let α(t) be the limiting ratio of the generalized Fibonacci numbers produced by summing along lines of slope t through the natural arrayal of Pascal’s triangle. We prove that √ α(t) 3+t is an even function. 1. Overview Pascal’s triangle may be arranged in the Euclidean plane by associating the binomial coefficient ij with the point 1 3 j − i, − i ∈ R2 2 2 √ (1.1) for all nonnegative integers i, j such that j ≤ i, as illustrated in Figure 1.1. The points in R2 associated...