Keyboard shortcuts

Press ← or → to navigate between chapters

Press ? to show this help

Press Esc to hide this help

Metadata 
bibkey: hanna2024a373312
authors: Paul D. Hanna
year: 2024
title: OEIS A373312, g.f. satisfying A(x)^2 = A(x*A(x)/(1-A(x))^2)
doi: null
url: https://oeis.org/A373312
claim: "Expansion of g.f. A(x) satisfying A(x)^2 = A( x*A(x)/(1 - A(x))^2 ). Conjecture: a(n) == 1 (mod 2) iff n = 2^k - 1 for k >= 1."
strata_touched:
  - D5/S1/Recurrence/Invariants/UnitReversionSquareParity
license: citation-only
triage: anchor

OEIS A373312

Paul D. Hanna’s entry, dated Jun 25 2024, specifies the generating equation A(x)^2 = A(x*A(x)/(1-A(x))^2) and states the parity conjecture quoted above. With the normalization A(0)=0 and a(1)=1, the Lean module constructs the unique integer solution and proves the conjecture for every positive index.

Verified locator

  • URL: https://oeis.org/A373312