2023/08/04 by Adegoke, Kunle, Frontczak, Robert, Goy, Taras
#Combinatorics (math.CO) #FOS: Mathematics #Primary 11B39 #Secondary 11B37
paper · doi:10.48550/arxiv.2308.04567
We explore new types of binomial sums with Fibonacci and Lucas numbers. The binomial coefficients under consideration are (n)/(n+k)\binomn+kn-k and (k)/(n+k)\binomn+kn-k. The identities are derived by relating the underlying sums to Chebyshev polynomials. Finally, some combinatorial sums are studied and a connection to a recent paper by Chu and Guo from 2022 is derived.