Finding explicit and/or recursive formula for the simple sequence $6, 15, 18, 19, ...$ Given the sequence $6,15,18,19,...,$ what is the recursive/explicit formula?

This is clearly not an arithmetic or geometric series but it does seem to satisfy:

\begin{align*}
u(1) &amp;= 6 \\
u(n) &amp;= u(n-1) + 9^{1/n}
\end{align*}

A general question:  Given only a few terms I would guess that my solution is not unique.  Is there any way to prove this other than by counter-example?

Are there any good strategies for determining these formulae other than intuition and trial&amp;error?

Thank you,
Chris
A sequence is just an ordered list of things; there doesn't necessarily have to be a single "nice" formula that goes with it. To show that your solution is not unique, just start listing other numbers. If we trust your recursive formula for the first few terms, the sequence could be 
$$
  6,15,18,19,0,0,0,0,0,\dotsc
$$ 
given by the rule
$$\begin{cases}
u(1) = 6 \\
u(n) = u(n-1) + 9^{1/n} \quad\forall x \in \{2,3,4\}\\
u(n) = 0 \quad\text{otherwise} 
\end{cases}$$
Note that is $+9,+3,+1$. You can complete as you want... For example $+9,+3,+1$ recursively, or $a_n=a_{n-1}+3^{4-n}$, etc