# Treble Trouble!

$\large 2^a + 2^b + 2^c$

We are given the natural numbers $$1\leq a \leq 100$$, $$1\leq b \leq 50$$, $$1 \leq c \leq 25$$. If the total possible number of ordered triplets $$(a,b,c)$$ such that the expression above is divisible by $$3$$ is $$k$$, evaluate $$k$$.

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