Pell–Padovan-circulant sequences and their applications
نویسندگان
چکیده
This paper develops properties of recurrence sequences defined from circulant matrices obtained from the characteristic polynomial of the Pell–Padovan sequence. The study of these sequences modulo m yields cyclic groups and semigroups from the generating matrices. Finally, we obtain the lengths of the periods of the extended sequences in the extended triangle groups E(2, n, 2), E(2, 2, n) and E(n, 2, 2) for n ≥ 3 as applications of the results obtained.
منابع مشابه
The upper bound estimation for the spectral norm of r-circulant and symmetric r-circulant matrices with the Padovan sequence
In this paper, we gives an upper bound estimation of the spectral norm for matrices A and B such that the entries in the first row of n×n r-circulant matrix A = Circr(a1, a2, . . . , an) and n×n symmetric r-circulant matrix B = SCircr(a1, a2, . . . , an) are ai = Pi or ai = P 2 i or ai = Pi−1 or ai = P 2 i−1, where {Pi}i=0 is Padovan sequence. At the last section, some illustrative numerical ex...
متن کاملClassical Sequences Revisited with Permutations Avoiding Dotted Pattern
Inspired by the definition of the barred pattern-avoiding permutation, we introduce the new concept of dotted pattern for permutations. We investigate permutations classes avoiding dotted patterns of length at most 3, possibly along with other classical patterns. We deduce some enumerating results which allow us to exhibit new families of permutations counted by the classical sequences: 2n, Cat...
متن کاملDeterminantal Representations for Generalized Fibonacci and Tribonacci Numbers
the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Using certain Hessenberg matrices, we provide some determinantal representations of the general terms of second-and third-order linear recurrence sequences with arbitrary initial values. Moreover, we provide explicit formu...
متن کاملExact Determinants of the RFPrLrR Circulant Involving Jacobsthal, Jacobsthal-Lucas, Perrin and Padovan Numbers
Circulant matrix family occurs in various fields, applied in image processing, communications, signal processing, encoding and preconditioner. Meanwhile, the circulant matrices [1, 2] have been extended in many directions recently. The f(x)-circulant matrix is another natural extension of the research category, please refer to [3, 11]. Recently, some authors researched the circulant type matric...
متن کاملThe Jacobsthal Sequences in Finite Groups
Abstract In this paper, we study the generalized order- Jacobsthal sequences modulo for and the generalized order-k Jacobsthal-Padovan sequence modulo for . Also, we define the generalized order-k Jacobsthal orbit of a k-generator group for and the generalized order-k Jacobsthal-Padovan orbit a k-generator group for . Furthermore, we obtain the lengths of the periods of the generalized order-3 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017