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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