<PRE><B>Question 982792</B>
&lt;pre&gt;
First I found the differences

2,12,36,80

I subtracted the squares 1,4,9,16 from those differences

1,8,27,64

I recognized those as the cubes.

So to get the next term, we add the square and the cube of the
number of the term

The recursion formula is

a&lt;sub&gt;n+1&lt;/sub&gt; = a&lt;sub&gt;n&lt;/sub&gt; + n&lt;sup&gt;2&lt;/sup&gt; + n&lt;sup&gt;3&lt;/sup&gt;, a&lt;sub&gt;1&lt;/sub&gt; = 1 
 
-------------------

Start with 1
Add 1&lt;sup&gt;2&lt;/sup&gt;+1&lt;sup&gt;3&lt;/sup&gt;, which is 1+1=2, get 3
Add 2&lt;sup&gt;2&lt;/sup&gt;+2&lt;sup&gt;3&lt;/sup&gt;, which is 4+8=12, get 15
Add 3&lt;sup&gt;2&lt;/sup&gt;+3&lt;sup&gt;3&lt;/sup&gt;, which is 9+27=36, get 51
Add 4&lt;sup&gt;2&lt;/sup&gt;+4&lt;sup&gt;3&lt;/sup&gt;, which is 16+64=80, get 131
Add 5&lt;sup&gt;2&lt;/sup&gt;+5&lt;sup&gt;3&lt;/sup&gt;, which is 25+125=150, get 281

Edwin&lt;/pre&gt;

</PRE>