(1+x)n=r=0∑n(rn)xr
Given the binomial expansion above, evaluate the value of
2[(0n)+(3n)+(6n)+⋯+(nn)]+(1+ω)[(1n)+(4n)+(7n)+⋯+(n−2n)]+(1+ω2)[(2n)+(5n)+(8n)+⋯+(n−1n)]
where
- ω denotes the non-real cube root of unity.
- n in an odd integral multiple of 3.
- (NM)=N!(M−N)!M! denotes the binomial coefficient.