Been staring at this for a few hours and I really need some help. The sequence is:
{4, 28, 148, 700, 3124, …}
According to google, the formula is: $$4(4^n – 3^n)$$
But I have zero idea how to come up with this on my own.
Any help or clues on how to solve this would be appreciated.
Thank you!
Best Answer
The formula would be correct if the sequence obeyed $$ x_{n+2} = 7 x_{n+1} - 12 x_n. $$ You can check that.
As far as a method, the relevant one is the "number wall" method in Conway and Guy, The Book of Numbers