Let \((1+x+x^2)^n = a_0 + a_1x + a_2x^2 + \ldots + a_{2n}x^{2n}\) be an identity in \(x\). If we let \(s = a_0 + a_2 + a_4 + \ldots + a_{2n}\), the original answer is in the form \(\frac{k \cdot 3^n + m}{n}\), where n cannot be divisible by 2. Please find the value of \(k + m + n\).

Let's think step by step and output the final answer within \boxed{}.
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