lean_workbook_plus_80993

⚠️ 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 solution for the recurrence relation $a_{n+2}=14a_{n+1}-a_n-4$ with initial conditions $a_1=a_2=1$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_80993 (a : ℕ → ℤ) (a1 : a 0 = 1) (a2 : a 1 = 1) (h : ∀ n, a (n + 2) = 14 * a (n + 1) - a n - 4) : ∀ n, a n = (2 ^ n + (-2) ^ n) / 3   :=  by sorry

The target shifts the initial indices and invents unrelated roots±2; use real arithmetic for the formula.

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 a₁=a₂=1 and use the characteristic roots r±=7±4√3: for n≥1, aₙ=1/3+(2/3)((1−r−)r+^(n−1)+(r+−1)r−^(n−1))/(r+−r−).

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.