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What are the next four numbers and the rule that generates the sequence?

0, 2, 8, 24, 64, 160, 384, 896, 2048, ...

Explain the hints and how you reached the answer once you have got it.

Hint 1:

The sequence continues indefinitely.

Hint 2:

These are all whole numbers. No fractions or negatives are in the sequence.

Hint 3:

Number representations are significant.

Hint 4:

Consider unusual math operations.

Hint 5:

Perhaps my own SE activity might be helpful...?

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Next four numbers are

4608, 10240, 22528, 49152

As the rule that generates the sequence is

$f(n) = n \times 2^n$

I got this simply because

There's a suspiciously high amount of powers of 2 in the sequence

But I have no idea what the hints mean.

OP's edit for further explanation and clarification:

My background is in programming, so the unusual operation is bitshifting, and my generating rule was to left-shift the binary representation of n by n bits.

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  • $\begingroup$ This works... but I agree. Perhaps he was looking for something different, since these aren't unusual operations. $\endgroup$
    – Shuri2060
    Commented Apr 6, 2016 at 18:52
  • $\begingroup$ @QuestionAsker If this isn't the answer, then you could argue that n<0 doesn't work for hint 2, and the 'real' sequence would. $\endgroup$
    – Lacklub
    Commented Apr 6, 2016 at 19:13
  • $\begingroup$ It's not quite the way I got the sequence, but I guess that is the formula. $\endgroup$
    – Jed Schaaf
    Commented Apr 6, 2016 at 19:58

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