Next-nearest-neighbor correlation formula conjecture

Let $N=2n+1$ be odd, and let $a_j$ denote the local observable used for the spin-chain correlations. Correlation formula conjecture. The next-nearest-neighbor correlation is

$$\langle a_j a_{j+2}\rangle=\frac{n-1}{4(2n-1)(2n+1)^2(2n+3)}\left[\frac{71}{4}n^3+\frac{149}{4}n^2+18n+9\right].$$

The expression is described as a fit to the available data rather than a derived identity, so its validity beyond the computed cases remains open.