Abstract We give Euler-like recursive formulas for the t -colored partition function when t=2 t = 2 or t=3, t = 3, as well as for all t -regular partition functions. In particular, we derive an infinite family of “triangular number” recurrences for the 3-colored partition function. Our proofs are inspired by the recent work of Gomez, Ono, Saad, and Singh on the ordinary partition function and make extensive use of q -series identities for (q;q) (q ; q) ∞ and (q;q) ³. (q ; q) ∞ 3.
Bhowmik et al. (Tue,) studied this question.