bibkey: hanna2026a338632
authors: Paul D. Hanna
year: 2026
title: "OEIS A338632, continued-fraction generating function with odd numerators"
doi: null
url: https://oeis.org/A338632
claim: "G.f. A(x) satisfies: 1 = A(x) - x/(A(x) - 3*x/(A(x) - 5*x/(A(x) - 7*x/(A(x) - 9*x/(A(x) - ...))))), a continued fraction relation. a(n) = 2 (mod 4) for n > 1 (conjecture)."
strata_touched:
  - D5/S1/Recurrence/Invariants/HannaA338632
license: citation-only
triage: anchor

OEIS A338632

Paul D. Hanna’s entry records the continued-fraction generating equation and the conjecture that every coefficient above degree one is two modulo four. The offset is zero and the initial data are 1, 1, 2, 14, 166, 2714, 55866, 1377942.

The formalization reads the continued fraction coefficientwise through its finite truncations. It proves existence and uniqueness of the normalized series and reduces the odd numerators modulo four to a quadratic equation. The normalized root is (1+x^2)/(1-x), whose coefficients above degree one are two modulo four.

Verified locator

DOI: null

Source: https://oeis.org/A338632