Hyperfibonacci Sequences and Polytopic Numbers
Ligia L. Cristea
Institute for Mathematics and Scientific Computing
University of Zagreb Faculty of Science
Zagreb University of Applied Sciences (former Polytechnic of Zagreb)
We prove that the difference between the nth hyperfibonacci number of
the rth generation and its two consecutive predecessors is the nth
regular (r-1)-topic number. Using this fact, we provide an equivalent
recursive definition of the hyperfibonacci sequences, and derive an
extension of the Binet formula. We also prove further identities
involving both hyperfibonacci and hyperlucas sequences, in full
Full version: pdf,
(Concerned with sequences
Received July 25 2015; revised versions received May 11 2016; September 1 2016.
Published in Journal of Integer Sequences, September 7 2016.
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