We study the growth at the golden rotation number ω = ( √ 5 − 1)/2 of the function sequence Pn(ω) = ∏n r=1 |2 sinπrω|. This sequence has been variously studied elsewhere as a skew product of sines, Birkho sum, q-Pochhammer symbol (on the unit circle), and restricted Euler function. In particular we study the Fibonacci decimation of the sequence Pn, namely the sub-sequence Qn = ∣∣∣∏Fn r=1 2 sinπ...

Abstract In this paper, we study a generalization of Narayana’s numbers and Padovan’s numbers. This also includes sequence whose elements are Fibonacci repeated three times. We give combinatorial interpretations graph interpretation these addition, examine matrix generators determine connections with Pascal’s triangle.

Fibonacci trees and generalized Fibonacci trees have been defined and studied by Horibe [4], Chang [2], and the author [1]. The k^ tree in the sequence of r-ary generalized Fibonacci trees, T(k), has T(k-c(i)) as the I leftmost subtree descending from its root node for k>r, and T(k) consists of a single root node for k-\ ...,r. Here c(i), z' = l,...,r, are positive integers with greatest common...

“FIBONACCI” directly implements the recurrence relation of the Fibonacci sequence. Each number in the sequence is the sum of the two previous numbers in the sequence. The running time is clearly O(n). The subproblem graph consists of n+ 1 vertices, v0, v1, ..., vn. For i = 2, 3, ..., n, vertex i has two leaving edges: to vertex vi−1 and to vertex vi−2. No edges leave vertices v0 or v1. Thus, th...

In this paper we introduce a family of infinite words that generalize the Fibonacci word and we study their combinatorial properties. We associate with this family of words a family of curves that are like the Fibonacci word fractal and reveal some fractal features. Finally, we describe an infinite family of polyominoes stems from the generalized Fibonacci words and we study some of their geome...

By Zeckendorf’s Theorem, every positive integer is uniquely written as a sum of non-adjacent terms the Fibonacci sequence, and its converse states that if sequence in integers has this property, it must be sequence. If we instead consider problem finding monotone with such call weak theorem. In paper, first introduce generalization Zeckendorf conditions, subsequently, theorems their converses f...

In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and search terms k-generalized Fibonacci sequence which repdigits. particular, find numbers powers 10 special case second part by using roots characteristic polynomial sequence, introduce tiny golden angles show feasibility new type in application to magnetic res...

A Fibonacci poem follows the sequence to any length in its count of syllables per line, or words lines stanza, other countable thing connected with poem. Fib is a special case poem, 6 whose syllable line first numbers sequence: 1; 2; 3; 5; 8. The present collection Fibs arose out Bridges poetry community response organization’s efforts make 2021 conference more interactive.

We investigate the solutions of certain meta-Fibonacci recurrences form $f(n)=f(n-f(n-1))+f(n-2)$ for various sets initial conditions. When $f(n)=1$ $n\leq 1$, we prove that resulting integer sequence is closely related to function c