lean_workbook_plus_406

⚠️ 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.

Let $f(n)$ be a sequence of integers defined by $f(1)=1, f(2)=1,$ and $f(n)=f(n-1)+(-1)^nf(n-2)$ for all integers $n \geq 3.$ What is the value of $f(20)+f(21)?$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_406 (f : ℕ → ℤ) (h₁ : f 1 = 1) (h₂ : f 2 = 1) (h₃ : ∀ n ≥ 3, f n = f (n - 1) + (-1 : ℤ) ^ n * f (n - 2)) : f 20 + f 21 = 1   :=  by sorry

The inserted recurrence value1 is wrong.

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

Proposed corrected statement

Under the source one-based recurrence prove f(20)+f(21)=89.

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.