Writing procedures

Posted on 2008-09-06 14:31 By bongiman (

24)

Categories:

How do I ...? with Maple (Student)

Hi,

I've written the following procedure and seem to have completely forgotten how to code in Maple!!

> restart:
> p:=proc(n,int)
> local k,s,i;
> for k from 2 to n do
> s[n]:= 2*sum(s[i]*s[n-i],i=1..n-2)+s[n-1]; end do:
> eval(s[n],n=k);
> end:
>
> p(2);p(3);p(4);p(5);p(10);

The above code yields results in terms of the expression s[i]. How do get my procedure to actually add it all up. For example p(10) should equal 103049? Many thanks.

encyclopedia

Comment on 2008-09-06 22:39 from Alex Smith ( Maple Rating 3

294)

Your code has a few peculiarities and obvious errors that make it hard to follow what you are trying to do, but the Encyclopedia of Integer Sequences shows a sequence whose tenth term is 103049, and one of the suggested formulae is quite close to the one you seem to be trying to use.

Based on this, maybe you want the following:

p:=proc(n::posint)
local k,s,i;
s[1]:=1;
s[2]:=1;
for k from 2 to n do
s[k]:=2*sum(s[i]*s[k-i],i=1..k-2)+s[k-1]; od;
s[n];
end;

p(10);

Many thanks Alex

Comment on 2008-09-08 18:23 from bongiman (

24)

I was so close but so far! :)

add

Comment on 2008-09-08 18:49 from acer ( Maple Rating 4

1377)

`add` is faster than `sum` for this sort of thing. It was about 2.5 times faster to compute p(2000) using `add` rather than `sum`, for example.

Writing a truly recursive procedure `s`, with option remember, is also faster than the above `sum` code (but not as fast as with `add`). But it could help, if you intend on computing some sorts of very long sets of increasing values with it.

s := proc(n)
local k;
option remember;
    if n = 1 or n = 2 then return 1
    else for k from 2 to n do
            s(k) := 2*add(s(i)*s(k - i), i = 1 .. k - 2) + s(k - 1)
        end do
    end if;
    s(n)
end proc:

So, once s(2000) is computed then s(1000) is computed near instantaneously, as it only requires a remember-table lookup.

I didn't bother considering whether there is any closed form of any of this.

acer