Given the other post Somos 3 Sequence i just wanted some insight to how the answer came around,
The Somos 3 sequence is:
$a_{n+3}a_n = a_{n+1}a_{n+2}$
Given $a_1=\alpha$ $a_2 = \beta$ and $a_3=\gamma$
How do you write the $a_n$ in terms of fixing it to $a_1,\ a_2,\ a_3$
And one of the answers wrote this:
$a_1,\ a_2,\ a_3,\ a_4=\frac{a_3a_2}{a_1},\ a_5=\frac{a_3^2}{a_1},\ a_6=\frac{a_3^2a_2}{a_1^2},\ a_7=\frac{a_3^3}{a_1^2},\ a_8=\frac{a_3^3a_2}{a_1^3},\ a_9=\frac{a_3^4}{a_1^3}$
And i was wondering how this came about.