bibkey: manyama2024a372018 authors: Seiichi Manyama; R. J. Mathar year: 2024 title: “OEIS A372018: an algebraic generating function and its odd-index conjecture” doi: null url: https://oeis.org/A372018 claim: “The entry defines A(x)=(1+4xA(x)/(1-xA(x)))^(1/2) and conjectures a(2n+1)=2*A371364(), with the argument missing in the published formula.” strata_touched:

• D5/S1/Recurrence/Algebraic/CubicOddBisection license: citation-only triage: anchor

OEIS A372018

Manyama submitted the sequence on April 15, 2024. Mathar’s formula dated April 22, 2024 explicitly labels the odd-index equality as a conjecture. The user approved reading the missing argument as n, consistently with the offset-zero definition of A371364 and the displayed sequence values. The formal statement uses that approved correction.

Squaring the defining equation and multiplying by 1-xA gives xA³-A²+3xA+1=0. The constant coefficient 1 fixes the square-root branch; 1-xA has constant coefficient 1, so this denominator is a unit. The repository constructs the series independently from this cubic. The entry attests the problem, not the proof supplied by the Lean module.

Verified locator

url: https://oeis.org/A372018

The internal page https://oeis.org/A372018/internal was retrieved and read on 2026-09-10. The NAME field states the generating equation. The FORMULA field reads “Conjecture: a(2n+1) = 2*A371364(). - R. J. Mathar, Apr 22 2024”. The OFFSET is 0,2. There is no DOI. The raw internal page is retained in the implementation attempt’s sources directory.