Mind Blown Again!?!?!?

Let \(x\) and \(y\) be non-negative integers. Suppose the number of strictly increasing sequences of integers \(a_{0},a_{1},a_{2}.................a_{2014}\) satisfying \(0≤a_{m}≤3m\) is \(2^{x}(2y+1)\). Find \(x\).

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