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Metadata 
bibkey: hanna2026a393172
authors: Paul D. Hanna
year: 2026
title: OEIS A393172, g.f. satisfying A(x-x^2) = x + A(x)^2
doi: null
url: https://oeis.org/A393172
claim: "G.f. A(x) satisfies A(x-x^2) = x + A(x)^2. Conjecture: for n > 1, a(n) == 2 (mod 4) iff n is a power of 2, otherwise a(n) is divisible by 4."
strata_touched:
  - D5/S1/Recurrence/Invariants/CatalanShiftSquareModFour
license: citation-only
triage: anchor

OEIS A393172

Paul D. Hanna’s entry of February 4, 2026 defines the integer coefficient sequence by A(x-x^2) = x + A(x)^2, with A(x) = x + ..., and states the quoted conjecture. The formalization addresses the normalized formal power series and the assertion for every index greater than one.

Verified locator

  • URL: https://oeis.org/A393172