lean_workbook_plus_77850

⚠️ 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 $A_n$ be the number of $n$ -digit numbers that do not end in a multiple of $3$ and $B_n$ be the number of $n$ -digit numbers that end in a multiple of three. Then, $A_{n+1}=5A_n + 6 B_n$ and $B_{n+1}=4A_n + 3B_n$ . Clearly, $A_1=6$ and $B_1=3$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_77850 (A B : ℕ → ℕ) (hA : A 1 = 6) (hB : B 1 = 3) (hA2 : ∀ n, A (n + 1) = 5 * A n + 6 * B n) (hB2 : ∀ n, B (n + 1) = 4 * A n + 3 * B n) : A 4 = 3168   :=  by sorry

The formal statement changes or incorrectly supplies part of the source problem; the accepted note identifies a concrete witness or definitional mechanism.

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

Proposed corrected statement

Retain the stated recurrences and initial values and prove A₄=3936, replacing 3168.

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.