A supercongruence for generalized Domb numbers

TL;DR

This paper proves a supercongruence for generalized Domb numbers, extending recent results and confirming a conjecture related to Zagier's sporadic solutions to certain differential equations.

Contribution

It introduces a new supercongruence for generalized Domb numbers, expanding the understanding of their arithmetic properties and linking to Zagier's solutions.

Findings

Proves a supercongruence for generalized Domb numbers

Extends previous results by Chan, Cooper, and Sica

Confirms a conjecture related to Zagier's sporadic solutions

Abstract

Using techniques due to Coster, we prove a supercongruence for a generalization of the Domb numbers. This extends a recent result of Chan, Cooper and Sica and confirms a conjectural supercongruence for numbers which are coefficients in one of Zagier's seven "sporadic" solutions to second order Apery-like differential equations.