On circulant like matrices properties involving Horadam, Fibonacci, Jacobsthal and Pell numbers

2021 ◽  
Vol 617 ◽  
pp. 100-120
Author(s):  
Enide Andrade ◽  
Dante Carrasco-Olivera ◽  
Cristina Manzaneda
Keyword(s):  
Pell Numbers

Pell Numbers, Pell–Lucas Numbers and Modular Group

2007 ◽  
Vol 14 (01) ◽  
pp. 97-102 ◽  
Author(s):  
Q. Mushtaq ◽  
U. Hayat
Keyword(s):  
Modular Group ◽  
Symmetric Matrix ◽  
Lucas Numbers ◽  
Lucas Number ◽  
Pell Numbers ◽  
The Matrix

We show that the matrix A(g), representing the element g = ((xy)2(xy2)2)m (m ≥ 1) of the modular group PSL(2,Z) = 〈x,y : x2 = y3 = 1〉, where [Formula: see text] and [Formula: see text], is a 2 × 2 symmetric matrix whose entries are Pell numbers and whose trace is a Pell–Lucas number. If g fixes elements of [Formula: see text], where d is a square-free positive number, on the circuit of the coset diagram, then d = 2 and there are only four pairs of ambiguous numbers on the circuit.

On the new Narayana polynomials, the Gauss Narayana numbers and their polynomials

2020 ◽  
pp. 2150100
Author(s):  
Engi̇n Özkan ◽  
Bahar Kuloğlu
Keyword(s):  
Hankel Transform ◽  
Pell Numbers ◽  
Pascal’S Triangle ◽  
Narayana Numbers ◽  
Definition Of ◽  
Pascal's Triangle ◽  
The Relationship ◽  
Derivatives Of

We give a new definition of Narayana polynomials and show that there is a relationship between the coefficient of the new Narayana polynomials and Pascal’s triangle. We define the Gauss Narayana numbers and their polynomials. Then we show that there is a relationship between the Gauss Narayana polynomials and the new Narayana polynomials. Also, we show that there is a relationship between the derivatives of the new Narayana polynomials and Pascal’s triangle. We also explain the relationship between the new Narayana polynomials and the known Pell numbers. Finally, we give the Hankel transform of the new Narayana polynomials.

scholarly journals On the Characteristic Polynomial of the Generalized k-Distance Tribonacci Sequences

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1387 ◽  
Author(s):  
Pavel Trojovský
Keyword(s):  
Characteristic Polynomial ◽  
Initial Conditions ◽  
Pell Numbers ◽  
Families Of Subsets

In 2008, I. Włoch introduced a new generalization of Pell numbers. She used special initial conditions so that this sequence describes the total number of special families of subsets of the set of n integers. In this paper, we prove some results about the roots of the characteristic polynomial of this sequence, but we will consider general initial conditions. Since there are currently several types of generalizations of the Pell sequence, it is very difficult for anyone to realize what type of sequence an author really means. Thus, we will call this sequence the generalized k-distance Tribonacci sequence (Tn(k))n≥0.

scholarly journals Symmetric and generating functions of generalized (p,q)-numbers

2021 ◽  
Vol 48 (4) ◽  
Author(s):  
Nabiha Saba ◽  
◽  
Ali Boussayoud ◽  
Abdelhamid Abderrezzak ◽  
◽  
...  
Keyword(s):  
Generating Functions ◽  
Fibonacci Numbers ◽  
Lucas Numbers ◽  
Pell Numbers ◽  
Lucas Polynomials ◽  
Binet’S Formula

In this paper, we will firstly define a new generalization of numbers (p, q) and then derive the appropriate Binet's formula and generating functions concerning (p,q)-Fibonacci numbers, (p,q)- Lucas numbers, (p,q)-Pell numbers, (p,q)-Pell Lucas numbers, (p,q)-Jacobsthal numbers and (p,q)-Jacobsthal Lucas numbers. Also, some useful generating functions are provided for the products of (p,q)-numbers with bivariate complex Fibonacci and Lucas polynomials.

scholarly journals Pell factoriangular numbers

2019 ◽  
Vol 105 (119) ◽  
pp. 93-100 ◽  
Author(s):  
Florian Luca ◽  
Japhet Odjoumani ◽  
Alain Togbé
Keyword(s):  
Pell Numbers

We show that the only Pell numbers which are factoriangular are 2,5 and 12.

scholarly journals The Om mani padme hum, the Platonic Soul, the Tao, and the Greek Cross are an Architectural Tool

1989 ◽  
Vol 22 ◽  
pp. 3-12
Author(s):  
Tine Kurent
Keyword(s):  
Good Description ◽  
Pell Numbers ◽  
Number Pattern ◽  
Composition I

The plan of Borobuclur conforms with two concentric octagrams. The lines of the scheme, their lengths, and their intersections, determine the articulation of the Borobudur composition, i. e. the sizes of every part and of the whole as well. The sizes of Borobudur are modular. Their modular multiples are Pell numbers, the ratios of which rationally approximate the irrational proportions in octagram  If Borobudur numbers are located in the Peli number-pattern and connected with a line, the syllable OM, written in Sanskrit, appears. The word octagram is only the modern European name of the symbol of OM. The prayer OM MANI PADME HUM, translated as 'the JEWEL and the LOTOS', is a good description of octagram.

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