Can you Identify a Pattern in this Sequence?

[FeDeX_LaTeX]

Hello;

Can you identify a pattern in this sequence of numbers (a recurrence relation)?

1, 3, 5, 9, 13, 17, 25, 33, 41, 49, 65, 81, 97, 113, 129, 161, 193, 225, 257, 289, 321, 385, 449, 513, 577, 641, 705, 769, 897, 1025, 1153, 1281, 1409, 1537, 1665, 1793, 2049, 2305, 2561, 2817, 3073, 3329, 3585, 3841, 4097, 4609, 5121, 5633...

I can sort of see a pattern but not a recurrence relation... if we look at how we can progressively get from term to term, it looks like this:

2¹ + 2¹ + 2² + 2² + 2² + 2³ + 2³ + 2³ + 2³...

So whenever you end up with a difference of 2ⁿ, you add that difference to any term n+1 times.

But generating a recurrence relation is more difficult...

Can you see a pattern?

 

[trambolin]

http://www.research.att.com/~njas/sequences/A007664

 

[FeDeX_LaTeX]

Hi;

Yes, I have looked at this page before and done a google search for my sequence too... But I already know about the Frame-Stewart algorithm and that page lists findings already described in my post. But I was just wondering if anyone here was able to find a better pattern that connects all the terms, such that a recurrence relation can be formed and solved.