bibkey: hanna2026a396102
authors: Paul D. Hanna
year: 2026
title: OEIS A396102, g.f. satisfying A(A(A(x))) = (1+x)*A(A(x))
doi: null
url: https://oeis.org/A396102
claim: "G.f. A(x) satisfies A(A(A(x))) = (1+x) * A(A(x)). Conjecture: a(n) == 1 (mod 3) for n >= 1."
strata_touched:
  - D5/S1/Recurrence/Invariants/TripleIterateShiftModThree
license: citation-only
triage: anchor

OEIS A396102

Paul D. Hanna’s entry, dated June 6, 2026, defines the generating series A(x) = x + ... by A(A(A(x))) = (1+x) * A(A(x)) and records the conjecture that every positive-index coefficient is congruent to one modulo three. The Lean module constructs the integer series, proves its defining equation and uniqueness with constant coefficient zero and linear coefficient one, and proves the conjecture for every positive index.

Verified locator

• URL: https://oeis.org/A396102