Some recurrence relations for binary sequence matrices

نویسنده

  • A. G. Shannon
چکیده

This note compares and contrasts some properties of binary sequences with matrices and associated recurrence relations in order to stimulate some enrichment exercises and pattern puzzles.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Recurrence Relations for Polynomial Sequences via Riordan Matrices

We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences of many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan matrices to interpret some relationships between different families of polynomials. Moreover using the Hadamard product of series we get a general recurrence ...

متن کامل

Characterizations of Quasiseparable Matrices and Their Subclasses via Recurrence Relations and Signal Flow Graphs

The three-term recurrence relations satisfied by real-orthogonal polynomials (related to irreducible tridiagonal matrices) and the twoand three-term recurrence relations satisfied by the Szegö polynomials (related to unitary Hessenberg matrices) are all well-known. In this paper we consider more general twoand three-term recurrence relations, and prove that the related classes of matrices are a...

متن کامل

Lower Bounds of Copson Type for Hausdorff Matrices on Weighted Sequence Spaces

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...

متن کامل

The Nonassociativity of the Double Minus Operation

The sequence A000975 in OEIS can be defined by A1 = 1, An+1 = 2An if n is odd, and An+1 = 2An + 1 if n is even. This sequence satisfies other recurrence relations, admits some closed formulas, and is known to enumerate several interesting families of objects. We provide a new interpretation of this sequence using a binary operation defined by a⊖ b := −a− b. We show that the number of distinct r...

متن کامل

Recursive three term recurrence relations for the Jacobi polynomials on a triangle

Given a suitable weight on IR, there exist many (recursive) three term recurrence relations for the corresponding multivariate orthogonal polynomials. In principle, these can be obtained by calculating pseudoinverses of a sequence of matrices. Here we give an explicit recursive three term recurrence for the multivariate Jacobi polynomials on a simplex. This formula was obtained by seeking the b...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012