The sequence (En\displaystyle {E}_{{n}}) is generated using a recursion rule similar to the Fibonacci, but it contains more terms
En+1=En+En1+En2\displaystyle {E}_{{{n}+{1}}}={E}_{{n}}+{E}_{{{n}-{1}}}+{E}_{{{n}-{2}}}.
What are the next five terms of this sequence if we have the seeds E0=1\displaystyle {E}_{{0}}={1}, E1=1\displaystyle {E}_{{1}}={1}, and E2=4\displaystyle {E}_{{2}}={4}.

E3\displaystyle {E}_{{3}} =
E4\displaystyle {E}_{{4}} =
E5\displaystyle {E}_{{5}} =
E6\displaystyle {E}_{{6}} =
E7\displaystyle {E}_{{7}} =