For questions about defining recursive functions, recursive algorithms and solving recursive equations.

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7
votes
2answers
308 views

How can I define a sequence of functions?

I need to define a function fun, and then re-define this function iteratively. The code is given at the end. First, a function ...
1
vote
1answer
217 views

How can I solve my recursion equation?

How can I solve the recursion equation given below? I doubt there have no solution for the recursion equation because this is circulating recucrsion equation. ...
3
votes
1answer
157 views

Converting this recursive function definition into nested sums?

Here's the recursive function I'm using: DH[n_, k_, s_] := Sum[Binomial[k, k - j] DH[n/m^j, k - j, m + 1], {m, s, n^(1/k)}, {j, 1, k}] DH[n_, 0, s_] := 1 Now, ...
6
votes
1answer
140 views

Recurrences of lists

Assume we have a multi-dimensional recurrence, e.g. $\qquad\begin{align*} a_1 &= (1,2) \\ a_n &= (1,2) + a_{n-1} \quad, n>1 \end{align*}$ with the easy solution $a_n = (n,2n)$. How ...
3
votes
2answers
157 views

Implementation of a recurrence relation for the polynomials appearing in the large order asymptotics of the Bessel functions

I would like to implement the recurrence relation for the polynomials $U_n(x)$ appearing in the large order asymptotics of the Bessel functions. The recurrence in question is ...
0
votes
2answers
120 views

Problem with Looping/Recurrence - Null Results [closed]

I'm trying to create a function that maps over a list of bits, and either returns the original bit or "mis-reads" the bit itself. The idea here is to simulate transcription errors. Here's the ...
1
vote
4answers
314 views

Recurrence relation in a table

I am trying to generate a list of x-values for a function using a module, where my x-value must increase by 'a' if the term ...
4
votes
0answers
110 views

Efficient Generation of Subgraphs (or, unfriend a friend a day)

NB: If you're not interested in the back-story, you could simply jump forward to the code which I'm seeking to optimize. Also, I believe this code would only work for MMA 8.0 and above. My friends ...
0
votes
0answers
30 views

Keeping memory to reduce the running time of recursion [duplicate]

I am using the following recursion in Mathematica to compute W[n, 1, s] for given n and s: ...
8
votes
5answers
267 views

Wrapping a function in count

I am working through the Programming Paradigms via Mathematica (A First Course) and am attempting to answer the following: Use recursion to count how many times the argument can have its square ...
8
votes
4answers
375 views

Partitioning a list by recursion (Programming Paradigms via Mathematica (A First Course))

I am working through the course Programming Paradigms via Mathematica. One of the homework exercises for the section Recursion I: Passing the Buck is as follows: Use recursion to partition a ...
1
vote
2answers
96 views

Using RecurrenceTable index to call elements of a vector

I am having trouble doing something that seems straightforward. I have a recursive sequence that I would like to produce which looks as follows: ...
1
vote
1answer
127 views

Recursive function taking functions as arguments

I'm trying to implement Lie brackets and derivatives of nth order. For doing this, I've stumbled upon something I don't understand. Here is an illustration: First I define the functions: ...
2
votes
1answer
350 views

Recursion depth exceeded

Below is my code for numerical solving of PDE with Crank Nicolson scheme. ...
4
votes
3answers
145 views

Modify this code using Module and While

I have written a recursive function and would like to re-write the code using Module AND While to compare the timings. Here is my recursive function for f[n], where 6 n f[n] = f[n-1] + n! for n>0 and ...
1
vote
3answers
247 views

List of Tribonacci Polynomials with Mathematica? [duplicate]

I want to list top ten of Tribonacci polynomials. I have following algorithm, but it doesnt work. ...
4
votes
1answer
108 views

RSolve gives a Context::ssle error

I want to solve the following recurrence equation RSolve[{(k + 2) c[k + 2] q^(k + 1) - c[k] == 0}, c[k], k] During calculation in Mathematica I get this ...
1
vote
1answer
236 views

Finding n-th term of a sequence of functions

Lets say, I have the following series of functions, $f_1=a+1$ $f_2=a^2+2a+1$ $f_3=a^3+3a^2+3a+1$ Assume that $f_4, f_5,$ and $f_6$ are also known. However $f_n$ is not known as a function of $n$. ...
5
votes
3answers
479 views

Implementing the Farey sequence efficiently

There is of course the silly implementation: FareySequence[n_] := Union[Flatten[Table[j/i, {i, 1, n}, {j, 0, i}]]] However, there are numerous properties and ...
2
votes
0answers
85 views

RSolve and incomplete gamma function

I am interested in how Mathematica uses the incomplete gamma function to solve difference equations. For example, if we have this inhomogeneous, 2nd order equation and use ...
2
votes
2answers
97 views

Rising Recursion Relationships

Lets say I want to compute the following function in mathematica: $G[n,k]=G[n+1,k-1] + G[n+2,k-2]$ where I know that $G[n,0]=n$ and $G[n,1]=n^2$. So, for example, $G[3,2]=G[4,1]+G[5,0]=4^2+5$ or, ...
3
votes
0answers
278 views

Solving recursion relations using Mathematica

I want to solve the recursion relation given in equation 2.7(a/b) on page $6$ of this paper. (..the initial seed is $F_1 = G_1 = 1$ and the functions $\alpha$ and $\beta$ are defined on page $5$ in ...
2
votes
0answers
185 views

Nonlinear recurrence relation

I entered the following recurrence relation into RSolve and it just gave the question back to me. $$a_{n+1} = \frac{(1+a_n +(a_{n−1})^3)} 3$$ Is there another way to get a formula for the nth term?
5
votes
0answers
193 views

Speeding up multilinear PRA branch-and-bound algorithm with worst-case exponential time scenario with respect to basic events

The algorithm is a branch-and-bound algorithm that calculates dominances for PRA, probalistic risk assessment. The task was to find faster ways to do it in numerical software such as Matlab but we ...
1
vote
1answer
147 views

Recursion evaluate Table power exceeded limit

I wrote 2 simple recursive functions for calculating the power of a table. pol3[Tb_List, n_Integer?Positive] := If[n == 1, Tb, Tb.pol3[Tb, n - 1]] and ...
5
votes
1answer
98 views

Recursion and safety of SetAttributes[Function, SequenceHold]

Compare the timings below ...
5
votes
2answers
204 views

Update a function avoiding infinite recursion

I am quite new to Mathematica and not completely familiar with functional programming. I am currently working with a function (call it foo) and wish to change its behaviour, for example, by adding 1 ...
24
votes
4answers
894 views

What tools can help in realizing tail recursion?

I had nice discussions with Leonid and Rojo that got me interested in tail recursion. Tail recursion is not always easy to realize with Mathematica, so it would be nice to have some tools to help with ...
2
votes
2answers
710 views

How to define functions for a parameter-dependent recursive sequence

I am trying to generate a two variable recursive sequence For instance on Mathematica, I did z[1] := {1, 1} B := {{t, 1}, {-1, t}} z[n_, t_] := B.z[n - 1, t] ...
1
vote
1answer
129 views

Unwanted hold in recursive function

I have a function (let it be called f) that does something useful for me and I want to be able to apply it to the elements of a list regardless of their depth and keep the list structure. For example ...
2
votes
1answer
95 views

Notation not recursive enough?

My notation is not recursing enough. For example, Notation[W[a_ | b_] ⟹ foo[a_, b_]/foo[b_]] Notation[W[a__, b_ | c_] ⟹ W[a__ | c_]W[b_ | c_]] Then ...
3
votes
1answer
116 views

Using NestWhileList to determine smallest prime value in series

I have a function recursively defined as follows: $a_{n+1}-1=(a_n-1)\times lpf(a_n)$, whe $lpf(x)$ is the least prime factor of $x$. Now, given an initial value of $a_0$, I would like to find the ...
3
votes
1answer
153 views

How to make a simple tree yourself with defined distances for each generation?

I'm trying to make a function that generates a tree for spin spin analysis in spectroscopy. I though it would be pretty easy, but I'm totally stocked. The tree should look something like this: ...
17
votes
3answers
570 views

How to clear parts of a memoized function?

I have a function of two variables, e.g.: f[a_, b_] := f[a, b] = something f[a - 1, b - 1] etc With the above code I used the concept of memoization to speed up ...
2
votes
0answers
179 views

Am I entering this 2-variable recurrence correctly?

I'm trying to solve this recurrence with two variables. ...
2
votes
1answer
151 views

How can I get the general term of this recurrence equations?

Following is the recurrence relation: a[1] = 1; a[n_] := a[n - a[n - 1]] + 1 Array[a, 28] I tried to use RSolve, but it ...
0
votes
1answer
169 views

Creating Recursive Sequences

Quite a simple question, I reckon, however, even quite an extensive search hasn't helped me. I want to define a recursively defined sequence that starts with defined ...
1
vote
0answers
180 views

RSolve doesn't solve this recurrence equation

RSolve[{1 == b ((c k[t - 1]^a - k[t])/(c k[t]^a - k[t + 1])) c a k[t]^(a - 1), k[1] == b, k[3] == a}, k[t], t] I tried to read the documentation in Help ...
5
votes
4answers
233 views

Can the general term my recurrence equations be written with Floor or Mod?

I want to know the formula for the general term of the following recurrence system. I guess it can be written with Floor or Mod. ...
2
votes
2answers
559 views

defining recursively a function with multiple if conditions

I am trying to recursively define a function which satisfies the following system of equations and which depends on two parameters $n$ and $l$, $$ \begin{align} A(x, n, l) &= F[ A(x,n-1,l) ]\\ ...
4
votes
1answer
127 views

RecurrenceTable with vector

Mathematica can do a RecurrenceTable with a vector, here is a simple example: RecurrenceTable[{x[n + 1] == 2* x[n], x[0] == {1, 2, 3}}, x, {n, 3}] with output ...
10
votes
4answers
268 views

Order items by closest to the previous

I have a list of 2D points (a table, imagine the data of a parametric plot shuffled) I would like to join the points with a line that starts from one of them and always goes to the closest one. I ...
4
votes
1answer
459 views

How do I use RSolve to solve a system of recurrence relations?

I am trying to solve a system of recurrence relations as follows. ...
3
votes
1answer
737 views

Solve pair of recurrence relations

[Corrected equations and added simple example] Can you solve a system of (loosely) coupled recurrence relations like this in Mathematica somehow? ...
3
votes
0answers
92 views

An recurrence equation that can be solved in version 7 but not in version 8

A friend of mine showed me this code sample: RSolve[{a[n] == a[n - 5] + 1, Sequence @@ Table[a[i] == 1, {i, 5}]}, a[n], n] // Timing It's solved by version 7 in ...
1
vote
2answers
211 views

While-Loop Linear Projection

I'm would like to do a linear progression for a recursive relation of a consumption function. Combining my program skills and my sparse knowledge of mathematica, I was thinking about doing it in a ...
3
votes
1answer
330 views

How to implement Condition programmatically?

I am writing my own symbolic functions with custom symbolic properties. So often I wish to introduce some automatic simplifications or evaluations, which return the same head as it's argument. This ...
9
votes
1answer
592 views

Compiling a recursive formula

My question is related to computing what is called "invariant measure" for a particular well known fractal - the Sierpinski triangle. We have an array m of four two by two matrices, say ...
2
votes
2answers
117 views

Recursion doesn't happen any more or doesn't happen correctly if I store the recursive relationship in a variable first

I know the following code will form a recursion: Clear["Global`*"] u[i_, n_] := u[i - 1, n] + u[i, n - 1] u[0, n_] := n u[i_, 0] := i u[2, 2] (* => 8 *) But ...
7
votes
2answers
367 views

How to deduce a generator formula for a polynomial sequence?

Consider a polynomial sequence $\{p_n\}$ generated by some (simple) rule: $$ \begin{array}{l} p_1(x)=x \\ p_2(x)=2 x-x^2 \\ p_3(x)= x^3-3 x^2+3 x \\ p_4(x)=-x^4+4 x^3-6 x^2+4 x \\ p_5(x)= x^5-5 ...