A real-world application of branching processes to a problem in cell biology where the generalized Fibonacci numbers known as k-nacci numbers play a crucial role is described. The k-nacci sequence is used to obtain asymptotics, computational formulas, and to justify certain practical simplifications. Along the way, an explicit formula for the sum of k-nacci numbers is established.
Taylor & Francis Ltd.
Olofsson, P., & Daileda, R.C. (2011). Budding yeast, branching processes, and generalized Fibonacci numbers. Mathematics Magazine, 84(3), 163-172. doi: 10.4169/math.mag.84.3.163