A sequence challenge

[James Hall]

The head of maths here has presented me with a sequence. It was apparently in an old year 7 question sheet, and it has flummoxed the entire maths department. What are the next few terms and/or what is the formula for the sequence?

Here it is:

1, 2, 6, 15, 16, 16, —15, —17

Any thoughts welcome!

[JackHurst]

I absolutely despise these sort of questions, there are infinitely many formulas that will generate that sequence of numbers, so how are you meant to know which one is the one the question setter was thinking of?

[Charlie Reams]

I absolutely despise these sort of questions, there are infinitely many formulas that will generate that sequence of numbers, so how are you meant to know which one is the one the question setter was thinking of?

Parsimony!

But yes, I agree.

[Hugh Binnie]

OEIS is flummoxed.

[JackHurst]

Bearing in mind my previous gripe, what comes next after 1, 2, 4, 8, 16?
Offer an explanation when you post your answer.

[Joseph Krol]

17 because it goes +1+2+4+8 and then repeats.

[Gavin Chipper]

I remember at school we did this thing drawing lines through a circle or something and it was 31.

[JackHurst]

I remember at school we did this thing drawing lines through a circle or something and it was 31.

Yeah, thats what I was thinking of.

http://www.uz.ac.zw/science/maths/zimaths/seq3132.htm

[Neil Zussman]

The head of maths here has presented me with a sequence. It was apparently in an old year 7 question sheet, and it has flummoxed the entire maths department. What are the next few terms and/or what is the formula for the sequence?

Here it is:

1, 2, 6, 15, 16, 16, —15, —17

Any thoughts welcome!

Nth term is:
x+
(x-1)(x-2)(3/2)+
(x-1)(x-2)(x-3)(1/3)+
(x-1)(x-2)(x-3)(x-4)(-5/8)+
(x-1)(x-2)(x-3)(x-4)(x-5)(A)+
(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(B)+
(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(C)+
(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8)(D)+
(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8)(x-9)(E)+...

Where A,B,C,D are numbers that can easily be worked out, one at a time following the pattern- in each step one more unknown enters the equations (the rest are all multiplied by 0), so it's simple, but time consuming to calculate them. And I reckon a year 7 could do that easily, provided they knew the right technique. It's very repetitive though, I imagine there's an easier way to generate such a sequence.
To answer the question, I think you can literally make the next number in the sequence whatever you like by changing E.

[Jon O'Neill]

Wat

[Hugh Binnie]

I remember at school we did this thing drawing lines through a circle or something and it was 31.

Yeah, thats what I was thinking of.
http://www.uz.ac.zw/science/maths/zimaths/seq3132.htm

Or 30, if it's factors of (n+1)!.

[Gavin Chipper]

Wat

I agree.

[John Gillies]

Would someone please solve this. I haven't a f****ing clue and it's driving me nuts!