Ramsey numbers of large even cycles and fans

For graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $N$ such that any red/blue edge coloring of $K_N$ contains either a red $F$ or a blue $H$. Let $C_n$ be a cycle of length $n$ and $F_n$ be a fan consisting of $n$ triangles all sharing a common vertex. In this paper, we prove that for all sufficiently large $n$, $$R(C_{2\lfloor an\rfloor },F_n)=\{\begin{array}{ll}(2+2a+o(1))n& \text{if }1\mathrm{/}2\le a<1\text{,}\\ (4a+o(1))n& \text{if }a\ge 1\text{.}\end{array}$$