bibkey: hanna2025a380711
authors: Paul D. Hanna
year: 2025
title: "OEIS A380711: generating function and parity conjecture"
doi: null
url: https://oeis.org/A380711
claim: "Conjecture: a(n) == binomial(3*n-1,n)/(3*n-1) (mod 2) for n >= 0."
strata_touched:
  - D5/S1/Recurrence/Algebraic/HannaAbsoluteCubicCongruence
license: citation-only
triage: anchor

OEIS A380711

Verified locator

Source: https://oeis.org/A380711

The entry is unpaginated. Its NAME states:

G.f. A(x) satisfies A(x) = 1 + x*A(x)*abs( 1/A(x)^3 ).

Its COMMENTS state:

Conjecture: a(n) == binomial(3n-1,n)/(3n-1) (mod 2) for n >= 0.

Absolute value is applied coefficientwise. The generalized binomial coefficient is Ring.choose over the integers, followed by rational division. At n = 0 the quotient is -1. The proposition asserts existence, coefficient integrality, quotient integrality, and congruence for every solution. The Fibbinary strengthening is not separately settled here.

Literature-screen completeness is ASSUMED-UNVERIFIED. The source and the screen recorded in issue #18828 are the literature boundary.