  Explicit algebraic area enumeration formulae are derived for various lattice
walks generalizing the canonical square lattice walk, and in particular for the
triangular lattice chiral walk recently introduced by the authors. A key
element in the enumeration is the derivation of some remarkable identities
involving 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 Ap\'ery-like numbers, the cousins
of the Ap\'ery numbers which play a central role in irrationality
considerations for {\zeta}(2) and {\zeta}(3).
