bibkey: hanna2023a363560 authors: Paul D. Hanna year: 2023 title: “OEIS A363560, g.f. satisfying A(x)^3 = 1 + x*(A(x) + A(x)^2 + A(x)^9)” doi: null url: https://oeis.org/A363560 claim: “Expansion of g.f. A(x) satisfying A(x)^3 = 1 + x*(A(x) + A(x)^2 + A(x)^9). Conjecture: a(n) == 0 (mod 3) for n > 0 except when n == 1 (mod 7).” strata_touched:

• D5/S1/Recurrence/Invariants/CubicNinthPowerSubstitutionModThree license: citation-only triage: anchor

OEIS A363560

Paul D. Hanna’s entry, authored August 12, 2023, defines the coefficients of the generating function by the cubic equation above, with constant term one. It conjectures divisibility by three at every positive index outside the residue class one modulo seven. The Lean module constructs the integer series, proves its defining equation and uniqueness, and proves this divisibility assertion. No nonvanishing assertion is made for the remaining residue class.

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• URL: https://oeis.org/A363560