# recognize the sequence numbers?

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.

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oeis.org – PAD Dec 26 '12 at 9:06
For typing text in Latex do \text{....} between two \$'s, Amir. – Babak S. Dec 26 '12 at 9:07
@Babak Sorouh ،Thank you. – Amir Alizadeh Dec 26 '12 at 10:54
@Amir: I have quite substantially re-formatted the question. If you like it, good. If not, feel free to either revert or improve. – arjafi Dec 26 '12 at 12:58
@ArthurFischer, the original form was good to copy and paste into Wolfram Alpha, which I did. – lhf Dec 26 '12 at 13:13

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...

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OEIS is very helpful , thank you so much. – Amir Alizadeh Dec 26 '12 at 10:49

Wolfram Alpha solves the first sequence with

and the second sequence with

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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.

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Thank you for correct the error. – Amir Alizadeh Dec 26 '12 at 10:41