lean_workbook_plus_57630

⚠️ 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.

Derive the recurrence relation $x_{n+2}=6x_{n+1} -x_n$ from the given $x_n = \frac{(3 + 2\sqrt{2})^n + (3 - 2\sqrt{2})^n}{2}$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_57630 (x : ℕ → ℝ) (hx: ∀ n:ℕ, x n = (Real.sqrt 2 + 3) ^ n + (Real.sqrt 2 - 3) ^ n) : ∀ n:ℕ, x (n + 2) = 6 * x (n + 1) - x n   :=  by sorry

Both conjugate bases and the factor 1/2 were mistranscribed.

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

Proposed corrected statement

Restore x_n=((3+2√2)^n+(3−2√2)^n)/2, then derive x_{n+2}=6x_{n+1}−x_n.

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.