  We derive the gravitational energy momentum tensor $\tau^{\eta}_{\alpha}$ for
a general Lagrangian of any order $L=L\left(g_{\mu\nu}, g_{\mu\nu,i_{1}},
g_{\mu\nu,i_{1}i_{2}},g_{\mu\nu,i_{1}i_{2}i_{3}},\cdots,
g_{\mu\nu,i_{1}i_{2}i_{3}\cdots i_{n}}\right)$ and in particular for a
Lagrangian such as $L_{g}=(\overline{R}+a_{0}R^{2}+\sum_{k=1}^{p}
a_{k}R\Box^{k}R)\sqrt{-g}$. We prove that this tensor, in general, is not
covariant but only affine, then it is a pseudo-tensor. Furthermore, the
pseudo-tensor $\tau^{\eta}_{\alpha}$ is calculated in the weak field limit up
to a first non-vanishing term of order $h^{2}$ where $h$ is the metric
perturbation. The average value of the pseudo-tensor over a suitable spacetime
domain is obtained. Finally we calculate the power per unit solid angle
$\Omega$ carried by a gravitational wave in a direction $\hat{x}$ for a fixed
wave number $\mathbf{k}$ under a suitable gauge. These results are useful in
view of searching for further modes of gravitational radiation beyond the
standard two modes of General Relativity and to deal with nonlocal theories of
gravity where terms involving $\Box R$ are present. The general aim of the
approach is to deal with theories of any order under the same standard of
Landau pseudo-tensor.
