Journal of Integer Sequences, Vol. 19 (2016), Article 16.3.6

On the Product Representation of Number Sequences, with Applications to the Family of Generalized Fibonacci Numbers

Michelle Rudolph-Lilith
Unité de Neurosciences, Information et Complexité (UNIC)
CNRS, 1 Ave de la Terrasse
91198 Gif-sur-Yvette


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.

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(Concerned with sequences A000045 A000129 A000290 A000578 A000583 A002378 A002522 A007531 A052762 A054602 A057721 A108299.)

Received September 1 2015; revised version received March 1 2016. Published in Journal of Integer Sequences, April 6 2016.

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