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How to find a mathematical formula for these points?

  1. Oct 12, 2008 #1
    how to find a mathematical formula for these points??

    i got these points for this function "b" :
    b(0,0)=1
    b(1,0)=3
    b(1,1)=4
    b(2,0)=8

    b(0)=1
    b(1)=2+1=3
    b(2)=4+1+3=8

    b(n)=2^n +b(0) +b(1) +b(2) +.. + b(n-2)+b(n-1)

    b(n-1)=2^n +b(0) +b(1) +b(2) +.. + b(n-2)

    b(n)=b(n-1)+b(n-1) =2*b(n-1)


    which by the way is wrong because b(1) doesn't equal to 2* b(0)

    b(n)=2*b(n-1)


    how to transform it to the formula
    b(n,c)=c+(n-2)*2^(n-1)


    ???
     
    Last edited: Oct 12, 2008
  2. jcsd
  3. Oct 12, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: how to find a mathematical formula for these points??

    You have both "b(0,0)" and "b(0)". Is b a function of one variable or two?

    Are you just trying to find a function that fits the points (and if so which points: (0,0,0) or (0,0)?) or do you have some other reason to believe that 2^n comes into the equataion?
     
  4. Oct 12, 2008 #3
    Re: how to find a mathematical formula for these points??

    every point ends with zero

    b(0,0)=b(0)
    b(1,0)=b(1)

    the reason i put 2^n into the equation is

    b(0)=1 b(0)=1
    b(1)=2+1=3 b(1)=2+b(0)
    b(2)=4+1+3=8 b(2)=4+b(0)+b(1)


    so each ne member is the sum of the previous members and 2^n

    unfortunately i dont know how build a standard formula from that series expression

    b(n,c)=c+(n-2)*2^(n-1)


    ???
     
  5. Oct 12, 2008 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: how to find a mathematical formula for these points??

    So this is NOT a problem of finding a formula that will give those points (there are an infinite number of formulas to fit any finite number of points) but of finding a "closed" formula for that iteration:
    bn= 2n+ b0+ b1+ ...+ bn-1 with b0= 1.
     
  6. Oct 12, 2008 #5
    Re: how to find a mathematical formula for these points??

    how do i find a "closed" formula for that iteration:
    bn= 2n+ b0+ b1+ ...+ bn-1 with b0= 1.

    so ill get

    b(n)=(n-2)*2^(n-1)

    ??
     
    Last edited: Oct 12, 2008
  7. Oct 12, 2008 #6
    Re: how to find a mathematical formula for these points??

    i simplified it into
    b(n)=2^(n-1) +2*b(n-1) b0=1

    what to do now
     
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