Explicit algebraic area enumeration formulae are derived for various lattice walks generalizing the canonical square lattice walks, and in particular for the triangular lattice chiral walks recently introduced by the authors. A key element in the enumeration is the derivation of some identities involving some remarkable trigonometric sums –which are also important building blocks of non trivial quantum models such as the Hofstadter model– and their explicit rewriting in terms of multiple binomial sums. An intriguing connection is also made with number theory and some classes of Apéry-like numbers, the cousins of the Apéry numbers which play a central role in irrationality considerations for $\zeta (2)$ and $\zeta (3)$.

推导了规范的方格结构的各种格结构，特别是作者最近引入的三角形格手性结构的显式代数面积枚举公式。枚举中的一个关键元素是一些恒等式的推导，这些恒等式涉及一些非凡的三角和，它们也是非平凡的量子模型（如霍夫施塔特模型）的重要构成部分，以及它们根据多个二项式和的显式重写。数论和一些类Apéry类数也构成了一种有趣的联系，Apéry类的表亲在非理性考虑中起着核心作用。$\zeta （2）$ 和 $\zeta （3）$。