bibkey: hanna2024a377100
authors: Paul D. Hanna
year: 2024
title: "OEIS A377100, a generating-function coefficient conjecture"
doi: null
url: https://oeis.org/A377100
claim: "G.f. A(x) satisfies A(x) = A(x^3)/A(x^2) + A(x)^2. Conjecture: a(n) == 1 (mod 3) for n >= 1, which has been verified for the initial 2305 terms."
strata_touched:
  - D5/S1/Recurrence/Invariants/HannaCubeSquareQuotientModThree
license: citation-only
triage: anchor

OEIS A377100

The unpaginated Name field states: “G.f. A(x) satisfies A(x) = A(x^3)/A(x^2) + A(x)^2.”

The unpaginated Comments field states: “Conjecture: a(n) == 1 (mod 3) for n >= 1, which has been verified for the initial 2305 terms.”

The example fixes the normalization A(0)=0, coefficient one at X, and offset one. The rational power-series statement includes existence and asserts that every positive coefficient is an integer congruent to one modulo three. The quotient is interpreted in the field of Laurent series.

Verified locator

Source: https://oeis.org/A377100