Factorizations of
Russell Jay Hendel · The Fibonacci Quarterly · 2007
We present one main result, the Factorization Theorem, which unifies several identities that exhibit factorizations of ∑n+i–1j=1Faj–b We introduce a unified proof method based on formulae for the factorization of Fq − d + Fq + d One of the factors of ∑n+i–1j=1Faj–b is a member of the second order recursive sequence whose members are {G1 + Ga + G2a + …} or (for a even) , with G equal L or F. It is shown that, for a even, these sequences obey the same recursions as the sequences {Gna}.