  A fan $F_n$ is a graph consisting of $n$ triangles, all having precisely one
common vertex. Currently, the best known bounds for the Ramsey number $R(F_n)$
are $9n/2-5 \leq R(F_n) \leq 11n/2+6$, obtained by Chen, Yu and Zhao. We
improve the upper bound to $31n/6+O(1)$.
