An Identity Generator: Basic Commutators - Farrokhi D. G., M. (The Electronic Journal of Combinatorics, 2008)
We introduce a group theoretical tool on which one can derive a family of identities from sequences that are defined by a recursive relation. As an illustration it is shown that _i=1^n-1F_n-iF_i^2 =12_i=1^n(-1)^n-i(F_2i-F_i) =F_n+12-F_n2, where {F_n} denotes the sequence of Fibonacci numbers.