Summary: We recall that the full susceptibility series of the Ising model, modulo powers of the prime 2, reduce to algebraic functions. We also recall the nonlinear polynomial differential equation obtained by Tutte for the generating function of the \(q\)-coloured rooted triangulations by vertices, which is known to have algebraic solutions for all the numbers of the form \(2+2\cos(j\pi/n)\), the holonomic status of \(q=4\) being unclear. We focus on the analysis of the \(q=4\) case, showing that the corresponding series is quite certainly non-holonomic. Along the line of a previous work on the susceptibility of the Ising model, we consider this \(q=4\) series modulo the first eight primes \(2,3,\ldots19\), and show that this (probably non-holonomic) function reduces, modulo these primes, to algebraic functions. We conjecture that this probably non-holonomic function reduces to algebraic functions modulo (almost) every prime, or power of prime numbers. This raises the question of whether such remarkable non-holonomic functions can be seen as a ratio of diagonals of rational functions, or even algebraic functions of diagonals of rational functions.