On the Product Representation of Number Sequences, with Applications to
the Family of Generalized Fibonacci Numbers
Unité de Neurosciences, Information et Complexité (UNIC)
CNRS, 1 Ave de la Terrasse
We investigate general properties of number sequences which allow
explicit representation in terms of products. We find that such
sequences form whole families of number sequences sharing similar
recursive identities. Applying the proposed identities to power
sequences and the sequence of Pochhammer numbers, we recover and
generalize known recursive relations. Restricting to the cosine of
fractional angles, we then study the special case of the family of
k-generalized Fibonacci numbers, and present general recursions and
identities which link these sequences.
Full version: pdf,
(Concerned with sequences
Received September 1 2015; revised version received March 1 2016.
Published in Journal of Integer Sequences, April 6 2016.
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