A note on fibonomial coefficients

2019 ◽  
Vol 60 (2) ◽  
pp. 143-153
Author(s):  
Víctor C. García ◽  
Florian Luca
Keyword(s):  
Fibonomial Coefficients

Closed form evaluation of sums containing squares of Fibonomial coefficients

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Emrah Kiliç ◽  
Helmut Prodinger
Keyword(s):  
Closed Form ◽  
Systematic Approach ◽  
Sums Of Squares ◽  
Lucas Numbers ◽  
Fibonomial Coefficients ◽  
Finite Products ◽  
Fibonacci And Lucas Numbers ◽  
Form Evaluation

AbstractWe give a systematic approach to compute certain sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. The technique is to rewrite everything in terms of a variable

scholarly journals Generalized Fibonacci Polynomials and Fibonomial Coefficients

2014 ◽  
Vol 18 (4) ◽  
pp. 541-562 ◽  
Author(s):  
Tewodros Amdeberhan ◽  
Xi Chen ◽  
Victor H. Moll ◽  
Bruce E. Sagan
Keyword(s):  
Fibonacci Polynomials ◽  
Fibonomial Coefficients

scholarly journals Some identities of Gaussian binomial coefficients

2022 ◽  
Vol Accepted manuscript ◽  
Author(s):  
Tian-Xiao He ◽  
Anthony G. Shannon ◽  
Peter J.-S. Shiue
Keyword(s):  
Binomial Coefficients ◽  
Recursive Sequences ◽  
Fibonomial Coefficients ◽  
Complete Functions ◽  
Gaussian Binomial Coefficients

In this paper, we present some identities of Gaussian binomial coefficients with respect to recursive sequences, Fibonomial coefficients, and complete functions by use of their relationships.

On sums related to the numerator of generating functions for the kth power of Fibonacci numbers on sums related to the numerator of generating functions for the kth power of Fibonacci numbers

2010 ◽  
Vol 60 (6) ◽  
Author(s):  
Pavel Pražák ◽  
Pavel Trojovský
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Fibonacci Numbers ◽  
Similar Type ◽  
Lucas Numbers ◽  
Fibonomial Coefficients ◽  
Sums Of Products

AbstractNew results about some sums s n(k, l) of products of the Lucas numbers, which are of similar type as the sums in [SEIBERT, J.—TROJOVSK Ý, P.: On multiple sums of products of Lucas numbers, J. Integer Seq. 10 (2007), Article 07.4.5], and sums σ(k) = $$ \sum\limits_{l = 0}^{\tfrac{{k - 1}} {2}} {(_l^k )F_k - 2l^S n(k,l)} $$ are derived. These sums are related to the numerator of generating function for the kth powers of the Fibonacci numbers. s n(k, l) and σ(k) are expressed as the sum of the binomial and the Fibonomial coefficients. Proofs of these formulas are based on a special inverse formulas.

Evaluation of sums containing triple aerated generalized Fibonomial coefficients

2017 ◽  
Vol 67 (2) ◽  
Author(s):  
Emrah Kiliç
Keyword(s):  
Fibonacci Number ◽  
Fibonomial Coefficients

AbstractWe evaluate a class of sums of triple aerated Fibonomial coefficients with a generalized Fibonacci number as coefficient. The technique is to rewrite everything in terms of a variable

scholarly journals Divisibility of Fibonomial coefficients in terms of their digital representations and applications

2022 ◽  
Vol 7 (4) ◽  
pp. 5314-5327
Author(s):  
Phakhinkon Napp Phunphayap ◽  
◽  
Prapanpong Pongsriiam
Keyword(s):  
Asymptotic Formulas ◽  
Digital Representations ◽  
Fibonomial Coefficients ◽  
Fibonomial Coefficient ◽  
Positive Integers

<abstract><p>We give a characterization for the integers $ n \geq 1 $ such that the Fibonomial coefficient $ {pn \choose n}_F $ is divisible by $ p $ for any prime $ p \neq 2, 5 $. Then we use it to calculate asymptotic formulas for the number of positive integers $ n \leq x $ such that $ p \mid {pn \choose n}_F $. This completes the study on this problem for all primes $ p $.</p></abstract>

Perfect powers among Fibonomial coefficients

2010 ◽  
Vol 348 (13-14) ◽  
pp. 717-720 ◽  
Author(s):  
Diego Marques ◽  
Alain Togbé
Keyword(s):  
Fibonomial Coefficients

On sums of squares of Fibonomial coefficients by q-calculus

2016 ◽  
Vol 09 (03) ◽  
pp. 1650062
Author(s):  
Emrah Kılıç ◽  
Aynur Yalçıner
Keyword(s):  
Closed Form ◽  
Generating Functions ◽  
Sums Of Squares ◽  
Classical Formula ◽  
Lucas Numbers ◽  
Fibonomial Coefficients ◽  
Finite Products ◽  
Fibonacci And Lucas Numbers ◽  
Form Evaluation

We present some new kinds of sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. As proof method, we will follow the method given in [E. Kılıç and H. Prodinger, Closed form evaluation of sums containing squares of Fibonomial coefficients, accepted in Math. Slovaca]. For this, first we translate everything into [Formula: see text]-notation, and then to use generating functions and Rothe’s identity from classical [Formula: see text]-calculus.

scholarly journals Fibonomial coefficients at most one away from Fibonacci numbers

2012 ◽  
Vol 45 (1) ◽  
Author(s):  
Diego Marques
Keyword(s):  
Fibonacci Numbers ◽  
Fibonomial Coefficients

AbstractLet

The p-adic order of some fibonomial coefficients whose entries are powers of p

2017 ◽  
Vol 9 (3) ◽  
pp. 228-235 ◽  
Author(s):  
Pavel Trojovský
Keyword(s):  
Fibonomial Coefficients
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