Some Linear Recurrences Motivated by Stern's Diatomic Array

2019/01/15 by Stanley, Richard P. · 2 citations
#05A15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.04647

Abstract

We define a triangular array closely related to Stern's diatomic array and show that for a fixed integer r≥ 1, the sum u_r(n) of the rth powers of the entries in row n satisfy a linear recurrence with constant coefficients. The proof technique yields a vast generalization. In certain cases we can be more explicit about the resulting linear recurrence.

Cited by

• Zeros of Stern polynomials in the complex plane
• Meeting a Challenge raised by Ekhad and Zeilberger related to Stern's Triangle

Related

• Proof of a conjecture of Stanley about Stern's array
• A closed formula for linear recurrences with constant coefficients
• Recurrence of Products of Linear Recursive Functions
• Definite Sums as Solutions of Linear Recurrences With Polynomial Coefficients
• Linear recurrences indexed by ℤ