how to find the nth number in the sequence? consider the sequence of numbers below,  


2 5 10 18 31 52 . . .  


the sequence goes on like this.
My Question is,
How to find the nth term in the sequence?
thanks.

The sequence can be expressed in many ways.
As Matt N. and M. Strochyk mentioned:
$$ a_{n+2}= a_{n}+a_{n+1}+3,$$
$$ a_1 = 2 \quad (n\in \mathbb{N})$$
Or as this one for example:
$$ a_{n+1}= a_{n}+\frac{(n-1)n(2n-1)}{12}-\frac{(n-1)n}{4}+2n+1,$$
$$ a_1 = 2 \quad (n\in \mathbb{N})$$
It's interesting that the term:
$$ b_n = \frac{(n-1)n(2n-1)}{12}-\frac{(n-1)n}{4}+2n+1$$ gives five Fibonacci numbers $(3, 5, 8, 13, 21)$ for $1 \leq n \leq 5$.
