A POLYNOMIAL ANALOGUE TO THE STERN SEQUENCE-Reference-Cited by-同舟云学术

A POLYNOMIAL ANALOGUE TO THE STERN SEQUENCE

Published:2007-03 Issue:01 Volume:03 Page:85-103
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

DILCHER KARL¹,STOLARSKY KENNETH B.²

Affiliation:

1. Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada

2. Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA

Abstract

We extend the Stern sequence, sometimes also called Stern's diatomic sequence, to polynomials with coefficients 0 and 1 and derive various properties, including a generating function. A simple iteration for quotients of consecutive terms of the Stern sequence, recently obtained by Moshe Newman, is extended to this polynomial sequence. Finally we establish connections with Stirling numbers and Chebyshev polynomials, extending some results of Carlitz. In the process we also obtain some new results and new proofs for the classical Stern sequence.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179304210700081X

Reference34 articles.

1. Proofs from THE BOOK

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