Sayan's Infinitely Many Ramanujan-Type Congruences for p_{3,1}(n) mod 3

*Author:* Sayan Kumar Mitra, Class 11, Rajendra Vidyalaya, Jamshedpur, Jharkhand — Independent Researcher *Abstract:* I proved infinitely many Ramanujan-type congruences for p_{3,1}(n) mod 3 via modular forms mod 3. Main result: p_{3,1}(l^k n + δ_k) ≡ 0 (mod 3). Let p_{3,1}(n) denote the number of mixed colored partitions of n: if a part is odd, it may be colored in one of three colors a,b,c; if a part is even, it carries exactly one color. Example: p_{3,1}(2)=7. This preprint is 15 pages and reviewed by Prof. George Andrews as "certainly worthy". Keywords: number theory, partitions, colored partitions, Ramanujan congruences, modular forms DOI: 10.5281/zenodo.23253216 arXiv categories: math.NT & math.CO, endorsement code: DUDVVA