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We determine all permutation trinomials of type $x^{2p^s+r}+x^{p^s+r}+\lambdax^r$ over the finite field $\mathbb{F}_{p^t}$ when $(2p^s+r)^4<p^t$. Thispartially extends a previous result by Bhattacharya and Sarkar in the case$p=2$, $r=1$.

On permutation trinomials of type $x^{2p^s+r}+x^{p^{s}+r} +\lambda x^r$