Keyboard shortcuts

Press ← or → to navigate between chapters

Press ? to show this help

Press Esc to hide this help

Metadata 
bibkey: hanna2024a374568
authors: Paul D. Hanna
year: 2024
title: OEIS A374568, g.f. satisfying x = A(x-x^2) - A(x+x^2)^2
doi: null
url: https://oeis.org/A374568
claim: "Expansion of g.f. A(x) satisfying x = A(x - x^2) - A(x + x^2)^2. Conjecture: a(n) is odd iff n = 4^k for k >= 0."
strata_touched:
  - D5/S1/Recurrence/Invariants/CatalanDoubleCompositionPowersOfFour
license: citation-only
triage: anchor

OEIS A374568

Paul D. Hanna’s entry, dated August 14, 2024, defines the coefficients of the normalized integer series satisfying x = A(x-x^2) - A(x+x^2)^2 and states the powers-of-four parity conjecture quoted above. The Lean module constructs the series, proves its uniqueness, and proves the conjecture for every positive index.

Verified locator

  • URL: https://oeis.org/A374568