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Math Help - Proving sequence formula - stellar numbers problem

  1. #1
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    Proving sequence formula - stellar numbers problem

    Hi,
    I've been working on a project based upon the idea of 'stellar numbers'. That is, a number which, when represented as dots, can be arranged into the shape of a star with p vertices. This leads to a sequence for each value of p, for example when p is 6 (i.e. a six pointed star) the first five terms (S1 to S5) would be:
    1, 13, 37, 73, 121....
    and when is 3:
    1, 7, 19, 37, 61...
    etc.
    I worked out the first eight terms of the sequences for five values of p and found a general statement: Sn = pn2 - pn + 1
    This obviously works for all terms I have actually found however I would like to know if there is a way that I can mathematically prove that this will work for any value of p or n (providing they're natural numbers of course). Or is this unnecessary? Impossible?
    Any help would be appreciated
    Thanks,
    jdbt
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  2. #2
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    Re: Proving sequence formula - stellar numbers problem

    you could try a proof by Mathematical induction
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