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Thanks a lot

Let N(1, 1)=1 and N(1,k)=0 if k<>1. Let N(s+1,k) = N(s,k) + N(s,k-1) + N(s,k+1).
Acting in such a way, we obtain  the triangle
         1
       1,1,1
    1,2,3,2,1
  1,3,6,7,6,3,1
.................,
where only the nonzero terms are shown.
What is the explicit formula for N(s,k)? How to find it with Maple?

Hello everyone

I want to check whether a recurrence relation produces integers. What I have written is rather messy, I ideally would like some kind of Proc where I can just put in the recurrence relation, the initial conditions and the number of terms I would like to check. Then get a result out which tells me whether the terms in the sequence are all integer. 

I have written the following (which tells me what I want to know but in a crude way)

I have a 3rd order nonlinear recurrence relation and I would like to produce the associated sequence.

Here is the relation x[n+2]:=(((x[n+1]*x[n])^2+x[n]^2+x[n+1]^3))/x[n-1]. At the moment the method I am using (a standard do command) is very computationally heavy when I want lots of iterates. I was wondering if there were faster loops, or procs.

Also I would like some kind of way to check if all the terms are integers, maybe some kind of summation where an...

(i^2+i*alpha+i*beta+i)*Q(n)+((-x*alpha-x*beta-2*x+beta-alpha)*n-x*alpha-x*beta-2*x+beta-alpha)*Q(n+1)+((1-x^2)*n^2+(-3*x^2+3)*n-2*x^2+2)*Q(n+2) = 0

After using diffeqtorec, there is n in coefficient, if multiply x^n/n! to all terms, i can not convert some to exponential function due to n^2, n and the difference of outer coefficient n not greater than n+2 in Q(n+2)

as i do not know the initial condition of above formula, differential equation is no use.

The June edition of the IBM Ponder This website poses the following puzzle:

Assume that cars have a length of two units and that they are parked along the circumference of a circle whose length is 100 units, which is marked as 100 segments, each one exactly one unit long.

A car can park on any two adjacent free segments (i.e., it does not need any extra maneuvering space).

there are several method to provide solve recurrence problems  in Maple,such as define ,rsolve,etc.here ,i meet a problem.

i want to compute the function Gamma(n), if n is a posint ,only given recurrence relation f(z)=(z-1)f(z-1),initial condition,f(0)=1,then i can get the true result with rsolve,of couse,i had made  an ansatz that z is n::posint.yet ,z is not posint? To suppose z  equal to 5/2, (2*n+1)/2 more generally,how can get the answer((2n-1)!!*Pi/2^n).

hello i  hope if you can help me.

 i have a problem solving this recurrence relation and how to insert if statemen (about  with for loop

and using the series and the solution should be

1-2y(2)-6y(3)-14y(4)=0

y(2)-y(3)-11y(4)=0;

-y(2)+3y(3)+8y(4)=0;

How to solve this receurrence relation with maple

I found various methods, as listen here http://en.wikipedia.org/wiki/Recurrence_relation, to solve recurrsion relation. For example, methods of undertermined coefficients

But how to use these to solve the the above recursive relation.

let us consider the series

y = a_0 - sum(a_i,i=1..n)

here the terms a_i are defined recurrsively as follows

a_i = (a_(i-1) -4*ln(x)/ln(10) + 4/10 + 4*ln(a_(i-1)) )/ ( 1+ 4/(a_(i-1) * ln(10)))

how can i program this in maple. so i can...