lean_workbook_plus_33888

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Find the closed form for $a_n=(3+2\sqrt 2)^n+(3-2\sqrt 2)^n$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_33888 (a : ℕ → ℝ) (a_n_def : ∀ n, a n = (3 + 2 * Real.sqrt 2)^n + (3 - 2 * Real.sqrt 2)^n) : ∃ a_n_closed_form, ∀ n, a n = a_n_closed_form   :=  by sorry

An index-dependent closed form was replaced by one scalar constant for every term.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

State an explicit function of n, e.g. the given power sum, or derive the recurrence a₀=2,a₁=6,aₙ₊₂=6aₙ₊₁−aₙ. Do not quantify a single real scalar as the closed form.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.