Find the next number in the sequence...

[wattie]

0, 1, 1, 2, 2, 3, 6, 7, N...

Really guys, it's very important to find the number N. All I can say for the moment is that N>=9 (but almost sure that N>9)

[Snark]

Where did this sequence come from?

There's an infinite number of sequences that would produce those first 8 numbers, but N would be different in most of the cases.

More background knowledge is needed to solve this problem.

Try this link to see if any of the sequences match what you're looking for.

[wattie]

Right, we can either use the Lagrange formula:

Spoiler:

0(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8) / ((1-2)(1-3)(1-4)(1-5)(1-6)(1-7)(1-8))+
1(x-1)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8) / ((2-1)(2-3)(2-4)(2-5)(2-6)(2-7)(2-8))+
1(x-1)(x-2)(x-4)(x-5)(x-6)(x-7)(x-8) / ((3-1)(3-2)(3-4)(3-5)(3-6)(3-7)(3-8))+
2(x-1)(x-2)(x-3)(x-5)(x-6)(x-7)(x-8) / ((4-1)(4-2)(4-3)(4-5)(4-6)(4-7)(4-8))+
2(x-1)(x-2)(x-3)(x-4)(x-6)(x-7)(x-8) / ((5-1)(5-2)(5-3)(5-4)(5-6)(5-7)(5-8))+
3(x-1)(x-2)(x-3)(x-4)(x-5)(x-7)(x-8) / ((6-1)(6-2)(6-3)(6-4)(6-5)(6-7)(6-8))+
6(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-8) / ((7-1)(7-2)(7-3)(7-4)(7-5)(7-6)(7-8))+
7(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7) / ((8-1)(8-2)(8-3)(8-4)(8-5)(8-6)(8-7)) = f(x)

or the Newtons method to interpolate it. The above equation simplifies to:

Spoiler:

f(x) = x^7/360-23x^6/240+193x^5/144-469x^4/48+28613x^3/720-1337x^2/15+1211x/12-43

Now we can find f(9):

Spoiler:

f(9) = 8

The problem - it's not 9 or larger than 9. So they are late! Very late! (see the spoiler below)

And of course you are right - there are infinite series which can be interpolated with the method above.

Where the problem came from? It came from...

Spoiler:

I want to find out when the punk band Exploited will release a new album The sequence contains the differences in years between their existing 8 albums. They did not release any album since 2003, so it has been 9 years already.

Don't kill me with stones guys. It's a real life problem. A big problem LOL

[jestingrabbit]

Fine, but its not a logic problem.

lock'd