recognize the sequence numbers?

Question

Is there software that can recognize the logical link between sequence numbers?

Example 1: $$\begin{array}{|l|c|c|c|c|c|c} \hline \text{sequence} & 2 & 6 & 12 & 20 & 30 & \cdots \\ \hline n & 1 & 2 & 3 & 4 & 5 & \cdots \\ \hline \end{array}$$ Here the $n$th term of the sequence is $n(n+1)$.

Example 2:

$$\begin{array}{|l|c|c|c|c|c|c|c} \hline \text{sequence} & 2 & 8 & 24 & 64 & 160 & 384 & \cdots \\ \hline n & 1 & 2 & 3 & 4 & 5 & 6 & \cdots \\ \hline \end{array}$$ Here the $n$th term of the sequence is $n 2^n$.

Thank you.

Answer 1

OEIS is excellent, the database is huge. If you don't have web access, you can also send an email. Results by an offline software are much more limited, but Mathematica has the FindSequenceFunction[] function. However, it doesn't seem to find your second example...

Answer 2

Your Second Sequence has error with 264 instead of 384.

OEIS is the best I know of:

http://oeis.org/search?q=2%2C8%2C24%2C64%2C160&sort=&language=english&go=Search

is very helpful to search sequences.

There might not be such offline softwares.

At least I don't know one.

Answer 3

Wolfram Alpha solves the first sequence with

http://www.wolframalpha.com/input/?i=2%2C6%2C12%2C20%2C30%2C...

and the second sequence with

http://www.wolframalpha.com/input/?i=2%2C8%2C24%2C64%2C160%2C384%2C...