We set the function f(n) (n is a positive integer) to be the number of different combinations of numbers from the above series to sum up to the n, for example:

f(11) = 3 because there are 3 ways you can make 11:

1 + 2 + 3 + 5 = 11

1 + 2 + 8 = 11

3 + 8 = 11

(you cannot use the same number twice)

Now let's set s(n) = f(1) f(2) + f(3) + ... + f(n), what is s(10^{17})?

I'll admit I got this as homework but I have a coding competition to attend and a holiday next week so I might not get time to try to solve it...

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Given the following Fibonacci sequence:

1 2 3 5 8 13 21 34 55 89

We set the function f(n) (n is a positive integer) to be the number of different combinations of numbers from the above series to sum up to the n, for example:

f(11) = 3 because there are 3 ways you can make 11:

1 + 2 + 3 + 5 = 11

1 + 2 + 8 = 11

3 + 8 = 11

(you cannot use the same number twice)

Now let's set s(n) = f(1) f(2) + f(3) + ... + f(n), what is s(10

^{17})?I'll admit I got this as homework but I have a coding competition to attend and a holiday next week so I might not get time to try to solve it...

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