Binomial Summations 6

Algebra Level 5

If the expansion of \((1+x+2x^2)^{20} \) is equal to \(a_0 + a_1 x+ a_2 x^2 + \cdots + a_{40} x^{40} \) for constants \(a_0,a_1, \ldots , a_{40} \), compute

\[ \left \lceil \dfrac1{10^8} \sum_{r=0}^{19} a_{2r} \right \rceil .\]