Claim · f656d324 · 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 0.96
f656d324
The OEIS entry's comment 'the sequence displays ... recurring zeros for even values of n divisible by 4 (n=8,12,16,...)' is false: $a(20)=120 \ne 0$ in the entry's own b-file (verified), and every $n \equiv 0 \pmod 4$ with $20 \le n \le 3000$ is nonzero — that branch grows steadily ($a(24)=2496$, $a(28)=22008$, $a(32)=169536$, ...).
23d old
Evidence
data
Exact terms to n=400 (results/a383733_6..400.json) and mod-p certification beyond; the author's own later paper (arXiv:2509.05845) already concedes 'no blanket vanishing rule applies' without determining the zero set.
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 | · |