Casimir elements and kernel of Weitzenb\"ok derivation

Let $k[X]:=k[x_0,x_1,\mathrm{.}\mathrm{.}\mathrm{.},x_n]$ be a polynomial algebra over a field $k$ of characteristic zero. We offer an algorithm for calculation of kernel of Weitzenb"ok derivation $d(x_i)=x_{i-1},\mathrm{.}\mathrm{.}\mathrm{.},$ $d(x_0)=0$, $i=\mathrm{1...}n$ that is based on an analogue of the well known Casimir elements of finite dimensional Lie algebras. By using this algorithm, the kernel is calculated in the case $n<7$.