PUMaC 2024 · 代数（A 组） · 第 6 题

PUMaC 2024 — Algebra (Division A) — Problem 6

Let { a } be the sequence defined by the recurrence relation a = 2 a − 23 a +3 a for n n +3 n +2 n +1 n n =0 3 all n ≥ 0, with initial conditions a = 20, a = 0, and a = 23. Let b = a for all n ≥ 0. Then 0 1 2 n n there exists a unique positive integer k and constants c , . . . , c with c ̸ = 0 and c ̸ = 0 0 k − 1 0 k − 1 P k − 1 such that for all sufficiently large n , we have the recurrence relation b = c b . Find n + k t n + t t =0 p p k + | c | + | c | . k − 1 0

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