pythonize this!

[Mark Lawrence]

On 18/06/2010 10:23, Andre Alexander Bell wrote:
> On 06/16/2010 12:47 PM, Lie Ryan wrote:
>> Probably bending the rules a little bit:
>>
>>>>> sum(x**2 - 8*x - 20 for x in range(1, 2010, 5))
>> 536926141
>
> Bending them even further, the sum of the squares from 1 to N is given by
>
> (1) N*(N+1)*(2*N+1)/6.
>
> The given problem can be divided into five sums of every fifth square
> starting from 1,2,3,4,5 respectively. This is given by
>
> (2) S(a,k) = sum_{i=1}^k (5*i-4+a)^2
>
> for a in range(5) and we are finally interested in
>
> (3) S(k) = S(0,k) + S(1,k) + S(2,k) - S(3,k) - S(4,k)
>
> Substituting (2) and (1) in (3) gives (in python code)
>
>>>> S = lambda k: (50*k**3 - 165*k**2 - 47*k) / 6
>>>> S(2010/5)
> 536926141
>
> However, this only works for full cycles of (1,1,1,-1,-1) and you would
> have to add/subtract the modulus parts yourself. (e.g. if you are
> interested in your sum from 1..2011...
>
> Cheers
>
>
> Andre

The good news is that this is easily the fastest piece of code that I've 
seen yet.  The bad news is that first prize in the speed competition is 
a night out with me. :)

Cheers.

Mark Lawrence.