2022/06/29 by Dougherty-Bliss, Robert
#05A15 #05A19 (Primary) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2206.14852
The Fibonacci numbers satisfy the famous recurrence Fn = Fn - 1 + Fn - 2. The theory of C-finite sequences ensures that the Fibonacci numbers whose indices are divisible by m, namely Fmn, satisfy a similar recurrence for every positive integer m, and these recurrences have an explicit, uniform representation. We will show that a(mn) has a uniform recurrence over m for any C-finite sequence a(n) and use this to automatically derive some famous summation identities.