Add to ORKGInternational audienceWe present a quite curious generalization of multi-step Fibonacci numbers. For any positive rational $q$, we enumerate binary words of length $n$ whose maximal factors of the form $0^a1^b$ satisfy $a = 0$ or $aq > b$. When $q$ is an integer we rediscover classical multi-step Fibonacci numbers: Fibonacci, Tribonacci, Tetranacci, etc. When $q$ is not an integer, obtained recurrence relations are connected to certain restricted integer compositions. We also discuss Gray codes for these words, and a possibly novel generalization of the golden ratio
Abstract. We look at a family of meta-Fibonacci sequences which arise in studying the number of leav...
The Fibonacci sequence is arguably the most observed sequence not only in mathematics, but also in n...
In number theory a very famous sequence of numbers is the Fibonacci sequence. It has the form 1, 1,2...
International audienceWe present a quite curious generalization of multi-step Fibonacci numbers. F...
We present a quite curious generalization of multi-step Fibonacci numbers. For any positive rational...
AbstractLet Φ be the golden ratio (√5 + 1)/2, fn the nth Fibonacci finite word and f the Fibonacci i...
19 pages, 5 figures, 3 tablesInternational audienceAn $n$-length binary word is $q$-decreasing, $q\g...
16 pages, 7 figures, 3 tablesA Sturmian word of slope q is the cutting sequence of a half-line y = q...
We give a combinatorial interpretation of the Fibonacci numbers, then use this interpretation as a t...
AbstractLet φ be the golden ratio. We define and study a continued φ-fraction algorithm, inspired by...
An n-color composition of n is a composition of n where a part k has k possible colors. It is known ...
Various generalizations of the Fibonacci numbers have been proposed, studied and ap-plied over the y...
Part 2: Regular PapersInternational audienceWe provide some interesting relations involving k-genera...
AbstractThe combinatorial properties of the Fibonacci infinite word are of great interest in some as...
The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 144 233 277, ...) is perhaps the most f...
Abstract. We look at a family of meta-Fibonacci sequences which arise in studying the number of leav...
The Fibonacci sequence is arguably the most observed sequence not only in mathematics, but also in n...
In number theory a very famous sequence of numbers is the Fibonacci sequence. It has the form 1, 1,2...
International audienceWe present a quite curious generalization of multi-step Fibonacci numbers. F...
We present a quite curious generalization of multi-step Fibonacci numbers. For any positive rational...
AbstractLet Φ be the golden ratio (√5 + 1)/2, fn the nth Fibonacci finite word and f the Fibonacci i...
19 pages, 5 figures, 3 tablesInternational audienceAn $n$-length binary word is $q$-decreasing, $q\g...
16 pages, 7 figures, 3 tablesA Sturmian word of slope q is the cutting sequence of a half-line y = q...
We give a combinatorial interpretation of the Fibonacci numbers, then use this interpretation as a t...
AbstractLet φ be the golden ratio. We define and study a continued φ-fraction algorithm, inspired by...
An n-color composition of n is a composition of n where a part k has k possible colors. It is known ...
Various generalizations of the Fibonacci numbers have been proposed, studied and ap-plied over the y...
Part 2: Regular PapersInternational audienceWe provide some interesting relations involving k-genera...
AbstractThe combinatorial properties of the Fibonacci infinite word are of great interest in some as...
The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 144 233 277, ...) is perhaps the most f...
Abstract. We look at a family of meta-Fibonacci sequences which arise in studying the number of leav...
The Fibonacci sequence is arguably the most observed sequence not only in mathematics, but also in n...
In number theory a very famous sequence of numbers is the Fibonacci sequence. It has the form 1, 1,2...