Since the generating function for \(1,2,3,4, \ldots\) is \(\frac{1}{(1-x)^2}\) and the generating function for \(1,2,4,8, 16, \ldots\) is \(\frac{1}{1-2x}\text{,}\) we have that the generating function for \(1,4, 11, 26, 57, \ldots\) is \(\frac{1}{(1-x)^2(1-2x)}\)
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