lean_workbook_plus_41120

⚠️ 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.

The function $S(N)=S(N-1)+S(N-2)+S(N-3).$ We can easily see that $S(1)=2,$ $S(2)=4,$ and $S(3)=8.$ We can then find a repeating pattern of $S(N)\mod 12$ and find that the answer is $\boxed{8}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_41120  (s : ℕ → ℕ)
  (h₀ : s 1 = 2)
  (h₁ : s 2 = 4)
  (h₂ : s 3 = 8)
  (h₃ : ∀ n, s (n + 3) = s (n + 2) + s (n + 1) + s n) :
  s 12 % 12 = 8   :=  by sorry

The source fragment does not identify the index that was being evaluated.

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

Proposed corrected statement

For the posted index12, replace the residue8 by6. Recover the source’s intended index before attaching its answer8.

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.