Coupled Fibonacci sequences of lower order have been generalized in number of ways.In this paper the Multiplicative Coupled Fibonacci Sequence has been generalized for r t h order with some new interesting properties. MSC: 11B39 • 11B37 • 11B99

a non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized fibonacci sequence , , , . a remarkable application of this definition may be find on the study of random covers in the cryptography. the 2-step generalized sequences for the dihedral groups studied for their pe...

For the familiar Fibonacci sequence | deened by f 1 = f 2 = 1, and f n = f n?1 + f n?2 for n > 2 | f n increases exponentially with n at a rate given by the golden ratio (1 + p 5)=2 = 1:61803398 : : :. But for a simple modiication with both additions and subtractions | the random Fibonacci sequences deened by t 1 = t 2 = 1, and for n > 2, t n = t n?1 t n?2 , where each sign is independent and e...

The “Fibonacci Dichotomy” of Kaiser and Klazar [15] was one of the first general results on the enumeration of permutation classes. It states that if there are fewer permutations of length n in a permutation class than the nth Fibonacci number, for any n, then the enumeration of the class is given by a polynomial for sufficiently large n. Since the Fibonacci Dichotomy was established for permut...

The Fibonacci groups F(n) are known to exhibit significantly different behaviour depending on the parity of n. We extend results for odd n family Fractional Fk/l(n). show that group Fk/l(n) is not fundamental an orientable hyperbolic 3-orbifold finite volume. obtain concerning existence torsion in (where odd) paying particular attention Fk(n) and Fk/l(3), observe consequences asphericity relati...

Abstract Prempreesuk, Noppakaew, and Pongsriiam determined the Zeckendorf representation of multiplicative inverse 2 modulo $$F_n$$ F n , for every positive integer n not divisible by 3, where denotes th Fibonacci number. We determine a fixed $$a \ge 3$$ <mml...

We have measured the angular dependence of ferromagnetic resonance (FMR) spectra for Fibonacci-distorted, Kagome artificial spin ice (ASI). The number strong modes in FMR depend on orientation applied DC magnetic field. In addition, discontinuities observed field-frequency dispersion curves also field orientation, and signal a multi-step magnetization reversal, which is caused by reduced energy...

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...

In lipid biochemistry, a fundamental question is how the potential number of fatty acids increases with their chain length. Here, we show that it grows according to the famous Fibonacci numbers when cis/trans isomerism is neglected. Since the ratio of two consecutive Fibonacci numbers tends to the Golden section, 1.618, organisms can increase fatty acid variability approximately by that factor ...