The Stern Diatomic Sequence via Generalized Chebyshev Polynomials. Issue 5 (1st May 2017)

• Record Type: Journal Article
• Authors: De Angelis, Valerio
• Is Part Of: American Mathematical Monthly. Volume 124:Issue 5(2017)
• Page Start: 451
• Page End: 455
• Publication Date: 2017-05-01
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.4169/amer.math.monthly.124.5.451
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: Let a ( n ) be the Stern diatomic sequence, and let x 1, …, xr be the distances between successive 1's in the binary expansion of the (odd) positive integer n . We show that a ( n ) is obtained by evaluating generalized Chebyshev polynomials when the variables are given the values x 1 + 1, …, xr + 1. We also derive a formula expressing the same polynomials in terms of sets of increasing integers of alternating parity and derive a determinant representation for a ( n ).