Hi guys, help me, please!

How can I generate this recurrence formula a

(0)=1;a(1)=0;a(2)=3;a(3)=1/6;for n=2:28;a(n+2)=((6/((n+1)*(n+2)))*sum(a(i)*a(n-i);i=0..n));end

[Walter Roberson]

Add one to each index, because you cannot use 0 as an index.

[Shadi Al-Ahmad]

Thank you

[Shadi Al-Ahmad]

Could you help me and write full code for my problem, please!

[James Tursa]

What is the text of your assignment?

[Walter Roberson]

a(0+1)=1;a(1+1)=0;a(2+1)=3;a(3+1)=1/6;for n=2:28;a(n+2+1)=((6/((n+1)*(n+2)))*sum(a(i+1)*a(n-i+1);i=0..n));end

Except that you need to figure out how to rewrite the sum(a(i+1)*a(n-i+1);i=0..n)) part . Hint: use .* instead of * and vectorize

[Shadi Al-Ahmad]

Still I have a problem

[Shadi Al-Ahmad]

This is called differential transform method for solving initial value problem

[Walter Roberson]

As I wrote, you need to figure out how to rewrite the sum(a(i+1)*a(n-i+1);i=0..n)) part. MATLAB does not offer any syntax for summation that uses variable=lower..upper notation (not unless you get fairly far into how the Symbolic Toolbox actually works.) MATLAB offers a symbolic summation of the form

symsum(SYMBOLIC_EXPRESSION, SYMBOLIC_VARIABLE, LOWER_BOUND, UPPER_BOUND)

however, the SYMBOLIC_VARIABLE cannot be used to index any array. symsum() is not intended for summation of a small finite number of terms: it is intended for creating formulas, such as

symsum(m^2, m, 1, n)

to get out the formula for the sum of squares of the first n numbers.

You need to find a different way to do the summation of indexed variables.

[Shadi Al-Ahmad]

Thank you Mr Walter

Answer 1

[James Tursa]

MATLAB indexing is 1-based, not 0-based. You will need to adjust your indexing:

a(1) = 1;
a(2) = 0;
  :
 etc

[Shadi Al-Ahmad]

Mr James, this is a part of solution of an initial value problem using differential transform method

[John D'Errico]

That is irrelevant. You cannot index a variable at index 0.

[Shadi Al-Ahmad]

Mr John, could you help me and write full MATLAB code for my problem, please?

[Walter Roberson]

You need to find a different way to do the summation of indexed variables.

Hint: use .* instead of * and vectorize

Hint:

>> A = [1 3 5 7]; A(1:3) .* A(2:4)
ans =
     3    15    35