Fibonacci Numbers in Pascal's Triangle

Date: 04/03/2003 at 18:27:59
From: Shortstuff
Subject: Fibonacci numbers in Pascal's Triangle

How do you find the Fibonacci numbers in Pascal's Triangle?

Date: 04/03/2003 at 18:57:38
From: Doctor Rob
Subject: Re: Fibonacci numbers in Pascal's Triangle

Thanks for writing to Ask Dr. Math, Shortstuff!

Add numbers along the diagonals of the triangle.

               1
             1   1
           1   2   1
         1   3   3   1
       1   4   6   4   1
     1   5  10  10   5   1
   1   6  15  20  15   6   1
        21  35  35  21   7   1
              70  56  28   8   1
                    84  36   9   1
                          45  10   1
                                11   1
                                       1

   1  + 21  + 70  + 84  + 45  + 11  +  1 = 233 = F(13)
       6  + 35  + 56  + 36  + 10  +  1 = 144 = F(12)
     1  + 15  + 35  + 28  +  9  +  1 =  89 = F(11)
         5  + 20  + 21  +  8  +  1 =  55 = F(10)

and so on.

Feel free to write again if I can help further.

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/