After the first term, this sequence is exactly the same as the Fibonacci sequence (with the first three terms truncated). Surely you can use the same formula to calculate terms . I.e. if the fibonacci sequence is and your sequence here is , set
What Gusbob said, of course!
But also you can apply the same ideas that lead to the "usual" Fibonacci formula. If you "look for" a solution of the form , the equation becomes . Dividing through by gives you or . Solving that . That is, for some constants A and B. That is exactly the solution you would get for the "usual" Fibonnacci formula. Putting and rather than setting them equal to the "usual" 1, 1, solve for A and b.