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Topic: How would I compute this?
Replies: 2   Last Post: Dec 14, 2017 11:50 PM

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Greg Heath

Posts: 6,387
Registered: 12/7/04
Re: How would I compute this?
Posted: Dec 14, 2017 11:50 PM
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On Monday, November 13, 2017 at 8:10:11 AM UTC-5, Aydon wrote:
> For some background information, I don't actually have formal training in math beyond arithmetic and I only found out that the sequence involved with my messing around is called the square pyramidal sequence after caving and asking someone two years ago.
>
> So as the above sentence suggests, there's game (equations? formula? function?) I've pen-and-papered with myself for years that involves the square pyramidal sequence.
>
> For example I take 3:
>
> 3 | 9 | 14
> And on one side of the paper, I'd write:
>
> 3
>
> 42
>
> The other side would have the variable in particular and might look like for example.
>
> 1
>
> 1.5
>
> The problems between these two would then go as follows:
>
> 9÷4.5=2
>
> 1÷(0.42)=2.38
>
> The 2.38 is greater than 2, so I'd change the 3 to a 4 on the one side of the paper and have:
>
> 4
>
> 1.2
>
> And the problems will go as:
>
> 16÷4.5=3.56
>
> 1÷1.2= 0.833.
>
> There's other rules I throw in to the game that is effectively a sort of pen and paper numbers simulation, but for now, if anyone can see the pattern I go through with here, what's a shorthand way to put these (functions? Formulas? Equations?) into code to reduce human error in sorting out my answers?
>
> I also apologize if I don't know whether to call these functions or formulas. Again, I don't have a lot of knowledge in math terminology.


As mentioned above, I don't have the slightest idea about what you are trying to do. However, I looked up the square pyramidal sequence and learned that the partial sums are just

S(n) = sum(i=1:n){ i^2 }

...

S1 = 1, S2 = 5, S3 = 14, S3 = 39,...

Greg





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