# [Edu-sig] Re: Idle play

André Roberge andre.roberge at gmail.com
Fri Apr 29 09:20:39 CEST 2005

```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

```