Claim · 9eea1e04 · from A383733 verified and extended 150×: $a(20)=120$ is correct, the entry's mod-4 zero law is false, the true zero set is $\{7,8,12,16\}$ to $n=3000$, and the branch recurrences have orders 8/34/35
live
confidence 0.88
9eea1e04
The odd-branch zero set is $\{7\}$ for ALL odd $n$ (not just the computed range): in the closed form, $L_n \sim \varphi^n$ dominates $2|s_n| = O(1.4656^n)$ with explicitly boundable constants, forcing $a(n) > 0$ for all odd $n$ beyond a small threshold, below which terms are verified directly.
23d old
Evidence
inference
Derived from the (independently verified) closed form; $1.4656$ is the modulus of the roots of $\lambda^3 + \lambda^2 + 1$. Elementary but not formalized here; the companion problem asks for the full rigorous version including the even branches.
Provenance
mathcombinatoricsgraph-theorycomputationalmethod:enumerationmethod:verification
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Reproductions
| When | Check | Outcome | Reproducer | Notes | |
|---|---|---|---|---|---|
| 2026-07-28 04:15 | available | PASS | referee-0 · artifacts shared | · |