Geodesic
Hyperfibonacci sequences and polytopic numbers
Journal of integer sequences, Tome 19 (2016) no. 7
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 
@article{JIS_2016__19_7_a5,
     author = {Cristea,  Ligia L. and Martinjak,  Ivica and Urbiha,  Igor},
     title = {Hyperfibonacci sequences and polytopic numbers},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {7},
     zbl = {1348.05024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a5/}
}
TY  - JOUR
AU  - Cristea,  Ligia L.
AU  - Martinjak,  Ivica
AU  - Urbiha,  Igor
TI  - Hyperfibonacci sequences and polytopic numbers
JO  - Journal of integer sequences
PY  - 2016
VL  - 19
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a5/
LA  - en
ID  - JIS_2016__19_7_a5
ER  - 
%0 Journal Article
%A Cristea,  Ligia L.
%A Martinjak,  Ivica
%A Urbiha,  Igor
%T Hyperfibonacci sequences and polytopic numbers
%J Journal of integer sequences
%D 2016
%V 19
%N 7
%U http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a5/
%G en
%F JIS_2016__19_7_a5
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/