## a look at recursive functions

Maple 13

Hi MaplePrimes,

another_recursive_sequence.mw

another_recursive_sequence.pdf

These two files have the same content.  One is a .pdf and the other is a Maple Worksheet.  I explore integer sequences of the form -

a(r) = c*a(r-1)+d*a(r-2) with a(1) and a(2) given.

Some of these sequences are in (the Online Encyclopedia of Integer Sequences) OEIS.org and some are not.  If we restrict c to 1 and assume that a(1)=1 and a(2) = 2 we have the parameter d remaining.  See additional webpage -

Let me know if you like the code.

Regards,

Matt

## How does one code a recursive sequence that depend...

Hi Mapleprimes people and robots,

My question is regarding a recursive sequence.  It can be defined non-recursively as -

a(r) :=  0.8*3^r + 0.2*(-2)^r.

The first few terms are -

1,2,8,20,68,188, and so on.

Here is my Maple Worksheet.
recursive_sequence_A133467.mw      recursive_sequence_A133467.pdf

I want some Maple code that will produce 30 terms of this sequence.  It is defined as

s[1]:=1:
s[2]:=2:

for n>2 we let s[n] = s[n-1] + 6*s[n-2].

Let me know if my question does not make sense.

Regards,
Matt

## How do I produce a sequence defined by a linear re...

In Mathematica, there is a command "LinearRecurrence" that lists a sequence generated by a linear recurrence.
For example,
LinearRecurrence[{-3, 1}, {7, 2}, 10]
will produce the first ten numbers in the sequence defined by a0=7, a1=2; a_n = -3 an-1 + an-2.

Is there anything similar in Maple?
If not, what would be the easiest way to do the same?

UPDATE: Two answers show how to do this example with rsolve, but it seems that this solution does not help in general for recurrence of high order.

Thank you.

## How to expand a double sum for a list of sequences...

Can somebody please expand the following double sum to produce a list of sequences?

(Sum(f[i], i = 0 .. 1))*(Sum(g[i, j, k], j = 0 .. 1)) for k = {1,2}

I need to make sure the operation order is correct, so I would like to verify my workings.

Thanks!

## Why doesn't this code works ? how can it work ?...

I'm trying to generate 100 equation to solve them numerically , buy maple won't let me , here's the code :

for i by 0 to 99 do
a := a[i]+a[i+1] = i^2
end do ;

## If-test of a sequence, why the need of `or`?...

Why do you need `or` in an if-test if say:

if `or`(seq(R[i]=R[k], k=1..i-1)) then
.......
end if;

If I run the test without the `or` (Boolean type logical, I know) it does not work.

Can anyone help me?

Hi all,
I have a question about editing strings in Maple2016.
When I make a variable "DataName" which is as below in Maple worksheet,
DataName:=Array(["Data1","Data2","Data3"]):

I want to make the variable "DataSet" whose elements are as below.
DataSet:=[1="Data1",2="Data2",3="Data3"]

Of course I can type the elements of "DataSet", but if the number of DataName increases, it requires a lot of time to do that, so I want to make the "DataSet" by using general command so that I can obtain "DataSet" automatically.
I tried to use the command "cat", "||", "map", and so on... but I could not find how to do that.
Is there anyone who can solve this problem? Please let me know how to solve this problem. I appreciate any idea you may have.

Always thanks for the nice answer

## Sequence minimize by fixed real number...

Dear all

I have n, p two integers greater than one

I would like to minimize the following real number by a fixed positive constant if its possible

`(n/(n+p))^(n/p)-(n/(n+p))^((n+p)/p)`

Many thanks

## How to update legend in display sequence of plots?...

I'm displaying a series of point plots as an animation, and would like to update a displayed parameter as well.  I have a nested list L[t] where there's a set of points for each t, and for each t there's also a numerical value M that I'd like to display.  (In my real problem, L[t] is the number of particles in each of several states, and M is the rms deviation from am algebraic probability distribution.)

The closest I've gotten (for a simple L and M) is the following, but it displays all of the M values in the legend at once:

with(plots); with(Statistics);

L := [[1, 2, 3, 4, 5, 6], [2, 4, 6, 8, 10, 12]];

M := [1, 2];

display([seq(PointPlot(L[t], legend = M[t]), t = 1 .. 2)], insequence = true)

I don't need this to be in the legend.  Is there a way to display only the current value of M for each t?  Thanks very much.

## Converting of seq - data to table / spreadsheet...

Hi,

I'm currently writing my thesis and actually haven't used Maple before.

I've got the following problem with converting the results of a sequence:

seq(Optimization:-Maximize(function with 2 variables), parameter:0..1,0.1)

The results are ok, but I can't convert the values to a spreadsheet with 4 columns (parameter value, maximum value, value of variable 1, value of variable 2).

Thank you!

Best regards

## How to use seq to make a sequence of functions?...

When using seq function below in the second call, it does not generate a sequence of functions with 'a' being 1, 2, and 3, and I had expected.

First seq function call is just to show that it works without the function "x ->" wrapping.

I could of couse use unapply as in the third call, but I had expected the second call to work.

Am I doing anything wrong, or is this a Maple bug?

## Fibonacci sequence...

Hello

Any idea about the summation of Fibonacci sequence

Fibonacci.mw

Best regards

## Creating a sequence of functions ...

i'm using maple in a research but i want to add a recursive function h_m(t) in 2 case : if m is integer positive and not,
la formule est donnée comme suit :
if (mod(m,1) = 0  and m>0) then  h:=proc(m,t)  local  t ;  h[0,t]:=t ;   for  i from -4 to  m  by  2 do  h [m,t]:= h[0, t]-(GAMMA(i/(2)))/(2*GAMMA((i+1)/(2)))*cos(Pi*t)*sin(Pi*t)  od:  fi:  end;
and i wanna to know how to programmate a Gaus Hypegeometric function. Thank You

## Checking a condition...

I need to do this with a sequence of a large number of elements but here is my question with a sequence of fewer elements.

a:={10,11,-13,9,20,74,10}:

I want to check each element of the sequence if it is negative. And if any element is negative I want to replace with 0 (or do something else). I tried the following code but it didn't work.

for k from 1 to 7 do
if (a[k]<0) then subs(a[k]=0, a) end if:
end do;

## Langford sequence...

Hello,

Paraphrasing:

https://en.m.wikipedia.org/wiki/Langford_pairing

given a sequence of 2n numbers 1,1,2,2,3,3,...n,n in which the two 1's are 1 slot apart, the two 2's are 2 slots apart, the two 3's are 3 slots apart, -> generally the two n's are n slots apart.

for n=3, a possible sequence is [2,3,1,2,1,3].

There is sequences for n=4,7,8...

i havent a clue how to write a maple procedure to generate a sequence for given n, but I'm hoping an expert here can.

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