My favorite integer sequence

[Gottfried]

I'm working on a set of generator polynomials that would allow me to compute an arbitrary term in the sequence in log-polynomial time. For instance, the naive approach requires O(n) calculations to calculate the nth term.
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I'll work on converting this to PARI/gp code, since I know that several of the active members of this forum seem to use that.

Wow, that's an ingenious approach. I was trying to arrive at a similar short-cutted computation-method using the idea of squaring the matrix M until sufficient few columns are relevant and only compute the required intermediate members of the sequence, but it seemed to become too complex and I left it for the time now. I'll be happy when I can try the Pari/GP-code....

I'll also be much interested if I can learn about the approach how to determine the function f(x) which prognoses/approximates the elements of the sequence. I could implement the function f(x) in Pari/Gp but just did not get the clue how one would arrive at it.
Gottfried