SOLUTION: 1, 3, 15, 51, 131, ? what the next in this and the logic please?

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Question 982792: 1, 3, 15, 51, 131, ?
what the next in this and the logic please?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
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

an+1 = an + n2 + n3, a1 = 1 
 
-------------------

Start with 1
Add 12+13, which is 1+1=2, get 3
Add 22+23, which is 4+8=12, get 15
Add 32+33, which is 9+27=36, get 51
Add 42+43, which is 16+64=80, get 131
Add 52+53, which is 25+125=150, get 281

Edwin
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