lean_workbook_plus_11951

⚠️ Retired — specification defect

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

Find the closed form for the sequence $a_n$ with the recurrence $a_{n+1} = 4a_n - a_{n-1}$ and initial terms $a_0 = 2, a_1 = 4$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_11951 (a : ℕ → ℝ) (a0 : a 0 = 2) (a1 : a 1 = 4) (a_rec : ∀ n, a (n + 1) = 4 * a n - a (n - 1)) : ∀ n, a n = (2 + √ 3) ^ n + (2 - √ 3) ^ n   :=  by sorry

The index-zero instance contradicts the two initial values.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

State the recurrence as a(n+2)=4a(n+1)−a(n), or restrict the displayed previous-index version to n≥1.

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.