Naslov
Hyperfibonacci sequences and polytopic numbers

Autori
Cristea, Ligia L. ; Martinjak, Ivica ; Urbiha, Igor

Izvornik
Journal of integer sequences (1530-7638) 19 (2016), 16.7.6; 1-13

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Fibonacci sequence; hyperfibonacci sequence; hyperlucas s equence; Binet for- mula; polytopic number

Sažetak
We prove that the difference between the $n$th hyperfibonacci number of the $r$th generation and its two consecutive predecessors is the $n$th 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 generality.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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