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