Every Third Binomial
Compute $\binom{30}{0} + \binom{30}{3} + \binom{30}{6} + \dots + \binom{30}{30}$, the sum of $\binom{30}{k}$ over all $k$ divisible by 3. Give an exact integer.
Related problems & prerequisites
Worth solving first
- Ten Planes 5.0/10
- Grid Paths 4.0/10
Source: Classic roots-of-unity filter exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.