EPISODE · Aug 24, 2025 · 5 MIN
OEIS A000317: Quadratic recurrence and integer polynomial binomial coefficients
from Intellectually Curious · host Mike Breault
We explore the nonlinear recurrence A_{n+1} = A_n^2 - A_n A_{n-1} + A_{n-1}^2, tracing its explosive growth, and explain Emmanuel Ferrand’s 2007 discovery that A000317 belongs to a special class whose generalized binomial coefficients are polynomials with integer coefficients. This reveals an elegant algebraic structure beneath a rapidly growing sequence, linking the recurrence to polynomial algebra and the idea of deformations of the Taylor formula.Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.Sponsored by Embersilk LLC
What this episode covers
We explore the nonlinear recurrence A_{n+1} = A_n^2 - A_n A_{n-1} + A_{n-1}^2, tracing its explosive growth, and explain Emmanuel Ferrand’s 2007 discovery that A000317 belongs to a special class whose generalized binomial coefficients are polynomials with integer coefficients. This reveals an elegant algebraic structure beneath a rapidly growing sequence, linking the recurrence to polynomial algebra and the idea of deformations of the Taylor formula. Note: This podcast was AI-generated,...
NOW PLAYING
OEIS A000317: Quadratic recurrence and integer polynomial binomial coefficients
No transcript for this episode yet
Similar Episodes
No similar episodes found.