lean_workbook_plus_43597

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Find the closed form of the sequence $a_n$ defined by the recurrence relation $a_{n+2} = a_{n+1} - 2a_n - 1$ with initial conditions $a_1 = 1$ and $a_2 = 3$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_43597 (a : ℕ → ℤ) (a1 : a 0 = 1) (a2 : a 1 = 3) (a_rec : ∀ n, a (n + 2) = a (n + 1) - 2 * a n - 1) : ∃ f : ℕ → ℤ, ∀ n, a n = f n   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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