lean_workbook_plus_67971

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

Find $d_{20}$ where $a_n=b_{n-1}+c_{n-2}$, $b_n=a_{n-1}$, $c_n=b_{n-2}$, $d_n=$ the sum of a, b, and c sub n, $a_1=1$, $b_1=1$, $c_1=2$, $a_2=2$, $b_2=1$, $c_2=2$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_67971 (a b c d : ℕ → ℕ) (h₁ : a = fun n => b (n - 1) + c (n - 2)) (h₂ : b = fun n => a (n - 1)) (h₃ : c = fun n => b (n - 2)) (h₄ : d = fun n => a n + b n + c n) (h₅ : a 1 = 1) (h₆ : b 1 = 1) (h₇ : c 1 = 2) (h₈ : a 2 = 2) (h₉ : b 2 = 1) (h₁₀ : c 2 = 2) : d 20 = 1513   :=  by sorry

Backward recurrences are imposed at zero and early indices despite incompatible supplied initial data.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Impose all three recurrences only at n≥3, retain the stated values at indices 1 and 2, and define d(n)=a(n)+b(n)+c(n). Recompute d(20) from this corrected initial-value system before selecting a numeral.

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.