The fifteenth term of an integer recurrence

Proved

WorkbookSource.problem_29548

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a_0 = 2$ , $a_1 = 9$ , and $a_n = 2a_{n - 1} - 4a_{n - 2}.$ Compute $a_{15}$ .

Source: InternLM Lean-Workbook, record lean_workbook_29548 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_29548 (a : ℕ → ℤ) (a0 : a 0 = 2) (a1 : a 1 = 9) (a_rec : ∀ n, n ≥ 2 → a n = 2 * a (n - 1) - 4 * a (n - 2)) : a 15 = -2^16  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_29548; Apache-2.0

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