A nonlinear recurrence sequence

formal-conjectures · oeis · ams-11

For even $n$, $a(n+2)$ is the greatest integer such that $a(n+2)/a(n+1) < a(n+1)/a(n)$;
for odd $n$, the least integer such that $a(n+2)/a(n+1) > a(n+1)/a(n)$;
$a(0) = 4, a(1) = 16$.

Conjecture: $a(n) = 4 a(n-1) - a(n-3) + a(n-4)$.
- Colin Barker, Feb 16 2012

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A022030
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/22030.lean
Local target: Corpus.OEIS22030.conjecture
Source SHA-256: 41b366c166da6dedab13397a6a9bcc549d4ef4ce238f610a9f0165e08165a106
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

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