Basic properties of a generalized third order sequence of numbers

2019/05/30 by Kunle Adegoke, Adegoke, Kunle
Physics and Astronomy · #11B37 #11B39 #FOS: Mathematics #Number Theory (math.NT) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1906.00788

openalex publication_date 2019/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the properties of the third order sequence (w_n)=(w_n(a,b,c; r, s,t)) defined by the recurrence relation w_n = rw_{n - 1} + sw_{n - 2} + tw_{n - 3} (n ≥ 3) with w₀ = a, w₁ = b, w₂=c, where a, b, c, r, s and t are arbitrary complex numbers and t≠ 0. Properties examined include the partial sum of the terms of the sequence, with indices in arithmetic progression, as well as double binomial summation identities.

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