Geodesic
Hyperfibonacci sequences and polytopic numbers
Journal of integer sequences, Tome 19 (2016) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 05A17, 11P84
Keywords: Fibonacci sequence, hyperfibonacci sequence, hyperlucas sequence, binet formula, polytopic number 
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     author = {Cristea, Ligia L. and Martinjak, Ivica and Urbiha, Igor},
     title = {Hyperfibonacci sequences and polytopic numbers},
     journal = {Journal of integer sequences},
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Cristea, Ligia L.; Martinjak, Ivica; Urbiha, Igor. Hyperfibonacci sequences and polytopic numbers. Journal of integer sequences, Tome 19 (2016) no. 7. http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a5/