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maths sequences help

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A sequence {un} is defined by u0 = 1, u1 = 2,

un+1 = 3un – 2un–1 – 1

where n ∈Z.

(a) Find u2, u3 and u4.

My book says that U2=4, U3=8 and U4=16. And that based on those numbers the formula for n is 2^n+1, which makes sense but what I dont get is how would you verify this formula to satisfy the equation (un+1 = 3un – 2un–1 – 1)?

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I think there is an error with the problem, because u2 should be 3(2) - 2(1) - 1 = 3, but the answer given is 4. Even then, the general un is 2^n not 2 ^(n+1) or 2^n + 1

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