  Let $\lambda_i (n)$ $i= 1, 2, 3$ denote the normalised Fourier coefficients
of holomorphic eigenform or Maass cusp form. In this paper we shall consider
the sum: \[ S:= \frac{1}{H}\sum_{h\leq H} V\left( \frac{h}{H}\right)\sum_{n\leq
N} \lambda_1 (n) \lambda_2 (n+h) \lambda_3 (n+ 2h)W\left( \frac{n}{N} \right),
\] \noindent where $V$ and $W$ are smooth bump functions, supported on $[1,
2]$. We shall prove a nontrivial upper bound, under the assumption that $H\geq
N^{1/2+ \epsilon}$.
