Binet's Formula for the Biperiodic Fibonacci sequence is given as
Yayenie, "The k-periodic Fibonacci sequence and extended Binet's formula," Integers, vol.
Hu Ning according to general relativity and Binet's formula
, we get the following improved Newton's formula of universal gravitation
states that as n [right arrow] [infinity], [F.sub.n] [right arrow] [[phi].sup.n]/[square root of 5]
Stakhov and Aranson trace the connection of the golden ratio, Fibonacci numbers, Lucas sequences, and Binet's formulas
with the "golden" hyperbolic Fibonacci and Lucas functions, Fibonacci </lambda>-numbers, and metallic proportions.