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Math Help - formula for counting triangles

  1. #1
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    Zewail University - Cairo - Egypt
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    Question formula for counting triangles

    i want a formula for counting triangles in a big triangle
    for example:

    level 1=1
    level 2=5
    level 3=13 and son on>>>

    plz help me
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  2. #2
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  3. #3
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    thank u very much for quick reply
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  4. #4
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  5. #5
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    Please check this

    When  n is odd , the formula is

     \binom{n+2}{3} + \frac{(n-1)(n+1)(2n+3)}{24}

    When n is even , it is

     \binom{n+2}{3} + \frac{n(n+2)(2n-1)}{24}

    Or generally the number of triangles we can count is  \binom{n+2}{3} + \frac{ n(n-1)(2n+5) + 6\lfloor{ \frac{n}{2} \rfloor}  }{24}


    Or  \frac{ n(n+2)(2n+1) + 2\lfloor{ \frac{n}{2} \rfloor}   - n }{8}
    Last edited by simplependulum; July 1st 2010 at 07:43 PM.
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