bibkey: hanna2016a274479
authors: Paul D. Hanna
year: 2016
title: "OEIS A274479, a generating-function coefficient conjecture"
doi: null
url: https://oeis.org/A274479
claim: "G.f. satisfies: A(x)^2 = A( x^2/(1 - 2*x - 4*x^2) ). a(n) = 1 (mod 3) for n>=1 (conjecture)."
strata_touched:
  - D5/S1/Recurrence/Invariants/HannaGeometricSquareSubstitutionModThree
license: citation-only
triage: anchor

OEIS A274479

The unpaginated Name field states: “G.f. satisfies: A(x)^2 = A( x^2/(1 - 2x - 4x^2) ).”

The unpaginated Comments field states: “a(n) = 1 (mod 3) for n>=1 (conjecture).”

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 inner rational function is X squared times the power-series inverse of its denominator.

Verified locator

Source: https://oeis.org/A274479