bibkey: hanna2026a396794
authors: Paul D. Hanna
year: 2026
title: OEIS A396794, G.f. A(x) satisfies A(x)*A(A(A(x))) = x^2 + 16*x^3
doi: null
url: https://oeis.org/A396794
claim: "G.f. A(x) satisfies A(x) * A(A(A(x))) = x^2 + 16*x^3. Conjecture: a(n) == 0 (mod 4) for n > 1."
strata_touched:
  - D5/S1/Recurrence/Invariants/TripleIterateProductModFour
license: citation-only
triage: anchor

OEIS A396794

Paul D. Hanna’s entry, dated June 7, 2026, defines the generating function by A(x) * A(A(A(x))) = x^2 + 16*x^3 and conjectures that a(n) == 0 (mod 4) for n > 1. The series starts at degree one with coefficient one. The Lean module constructs an integer series with this normalization, proves its defining equation and uniqueness, and proves the stated divisibility.

Verified locator

• URL: https://oeis.org/A396794