[Edu-sig] Re: Idle play

[André Roberge]

Kirby Urner wrote:
[snip...]
> 
> Adding n consecutive layers of this Christmas Tree gives n**3.
> 

The first thing that came to my mind is Pascal's triangle; adding the 
number on the n_th line gives 2^n.


> We looked up Tetra here:
> 
> http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?An
> um=A000292
> 
Great link!  I especially like, given my previous observation, the 
following:

=====
            Consider the square array
            1 2 3 4 5 6...
            2 4 6 8 10 12...
            3 6 9 12 16 20...
            4 8 12 16 20 24...
            5 10 15 20 25 30...
            ...
            then a(n) = sum of n-th antidiagonal. - Amarnath Murthy
               (amarnath_murthy(AT)yahoo.com), Apr 06 2003
=====

I was thinking a few days ago of writing a *recursive* function to 
create Pascal's triangle ... as an alternative example to the 
traditional Fibonacci's numbers.   I suspect (and will have to spend 
some time reading!) that the link you gave may provide a lot of 
potential examples of recursive functions.  I always found that, using
only fib(n) as an example of recursion was not very inspiring.

André