I have a problem today where I think I Iack of theory for solving it and hence I came here to ask for your help. The problem is the following :
find the general term of the sequence $$ x_{n+1} = x_n^2 + 1$$ where $x_0 = 3$.
I know how to solve for linear recurrence relations but I'm a bit lost here. I thank you in advance for the answers you shall give me.
The OEIS sequence A062013 is given by $\, a_1 = 3,\quad a_n = a_{n-1}^2+1.\,$ This sequence has a power series formula ($B(x)$ as appears in OEIS sequence A088674) given by $$ a_n = B(x) = \frac1{2x} - x - 3 x^3 - 6 x^5 - 45 x^7 - \dots\; \text{ where } x = \frac1{2c^{2^n}}, \; c \approx 1.7805035.$$