I have a sequence of numbers like this one:
$a_n = \{1, 10, 66, 406, 2454, \dots\}$
This sequence is not on OEIS, but I know that this is a geometric sequence of this form:
$a_n = b_1 A_1^n + b_2 A_2^n +\dots$
Is there a way to compute the multipliers $A_1,A_2,\dots$ using only a finite number of terms in the sequence (I don't care what the coefficients $b_1,b_2,\dots$ are)? How many terms would be needed if I knew how many $A_n$'s are in the formula?
As @JMoravitz commented, if you know the number of terms to be added, you could easily do it using regression.
For the fun of it, using your data $$a_n=\text{Round}\left[\alpha\, A^n+\beta\, B^n\right]$$ with $$(\alpha,\beta)=\frac{623511\pm19883 \sqrt{6598}}{1184341}\qquad \qquad(A,B)=\frac{141\pm\sqrt{6598}}{37} $$ will generate $$\{1,10,66,406,2454,14764,88716,532911,3200855,19225031,\cdots\}$$