The Almkvist-Zudilin supercongruence

Let $\mathbb{N}^+$ denote the positive integers, let $a_i(n)$ be the sequence defined by

$$a_i(n)=\sum_{k=0}^{\lfloor(n-i)/3\rfloor}(-1)^{n-k}\binom{3k+i}{k}\binom{2k+i}{k}\binom{n}{3k+i}\binom{n+k}{k}3^{n-3k-i},$$

and let $p\geq 5$ be prime. The Almkvist-Zudilin supercongruence. For every $n\in\mathbb{N}^+$,

$$a_0(pn)\equiv_{p^3}a_0(n).$$

This is the principal supercongruence for the Almkvist-Zudilin numbers, extending the type of congruences known for Apéry-type sequences. Its status is not resolved by the supplied source context.