Keyboard shortcuts

Press ← or → to navigate between chapters

Press ? to show this help

Press Esc to hide this help

Metadata 
bibkey: hanna2025a389540
authors: Paul D. Hanna
year: 2025
title: OEIS A389540, g.f. satisfying A(x)^2 = A(2*x - 2*A(x))/2
doi: null
url: https://oeis.org/A389540
claim: "G.f. A(x) satisfies A(x)^2 = A(2*x - 2*A(x)) / 2. Conjecture: a(n) is odd iff n = 2^k for k >= 0."
strata_touched:
  - D5/S1/Recurrence/Invariants/HalfScaledReflectionParity
license: citation-only
triage: anchor

OEIS A389540

Paul D. Hanna’s entry defines the generating function by A(x)^2 = A(2*x - 2*A(x))/2 and states the conjecture that its odd coefficients occur exactly at powers of two. The Lean module constructs the normalized integer series, proves its defining equation and uniqueness, and proves the parity assertion for every positive index.

Verified locator

  • URL: https://oeis.org/A389540