Here's a challenge for all the math's wiz of the world!?

Question

Find the sum of :
1 + 3 + 7 + 14 + 27 + 52 + .......(upto n terms)
This is quite a difficult problem but there is a trick of solving it. I don't need any detailed explaination as it will be really tiresome to type the entire solution. Just give me the answer. First person bags 10 points. you don't need to be any genius to solve it as i was able to solve it myself.

Answer 1

I had to look this one up in the Integer Sequence Database...

It's the Binomial transform of Thue-Morse sequence

So the sum is:
Σ[from k=0 to n] {(-1)^k * (n choose k)* a[k]}

Where a[k] is the Thue-Morse sequence:
http://www.research.att.com/~njas/sequences/A001285

Wow! Very tough!

Answer 2

a+n^2=b

Answer 3

104