lean_workbook_plus_17771

⚠️ 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.

Assuming this is true, then just use induction. Obviously it's true for $n=3$ , so assume it's true for $k\geq3$ . Then: $b_{k+1} = b_k + b_{k-1} + 2b_{k-2} + ... + 2b_0$ $b_{k+1} = b_k + b_{k-2} + \left[b_{k-1} + b_{k-2} + ... + 2b_0\right]$ $b_{k+1} = b_k + b_{k-2} + b_k$ (due to the assumption that it's true for $k$ ) $b_{k+1} = 2b_k + b_{k-2}$ $\square$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_17771  (b : ℕ → ℕ)
  (h₀ : b 0 = 0)
  (h₁ : b 1 = 1)
  (h₂ : ∀ n, b (n + 2) = b (n + 1) + b n + 2 * b (n - 1)) :
  ∀ n, b (n + 1) = 2 * b n + b (n - 1)   :=  by sorry

The source uses a finite sum and concludes b_{k+1}=2b_k+b_{k−2}; the target replaces that recurrence and uses the wrong index.

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 the exact finite-sum recurrence and its base indices, then prove b_{k+1}=2b_k+b_{k−2} for k≥3.

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.