# Questions tagged [integer-sequence]

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### Unexpected behavior of FindGeneratingFunction

FindGeneratingFunction will give up to computer sometimes?Such as FindGeneratingFunction[{1, 4, 6, 4, 1}, x] But actually the ...
384 views

### Generate the Fibonacci sequence with Accumulate

Is there a way to generate the Fibonacci sequence with the Accumulate function?
377 views

### Find the Kimberling Sequence

How to find the Kimberling Sequence by using Mathematica? each row is obtained from the previous by boxing (and expelling) the main diagonal element, and then reading the first number after the box,...
84 views

### Why does the FindSequenceFunction command sometimes succeed with subsequences, while failing for the longer sequences?

I've encountered this phenomenon a number of times--and can provide specific examples if requested. For example, I have a 75-long sequence of rational numbers for which the FindSequenceFunction fails ...
164 views

### Finding recurrence formulas from procedural code and output lists associated with integer sequences

This code outputs 37 sequences and takes about 15-minutes to run. I would like to be able to see how many and which variables { i, j, k, m, n } each of the 37 ...
82 views

49 views

### A problem of a sequence and its sum

{a(n)} is such a sequence, satisfying, For all a(i) ∈ {a(n)}, a(i) =1 or -1 Let S(j) = Sum[a(i) , {i ,1, j}], then for all 1<=j<=n ,S(j)>=0. For a given n , how many {a(n)} are there?
65 views

### How to postulate a formula for the following Mathematica function

I am using Mathematica to explore the properties of the Fibonacci Sequence. Below is the functions I have defined ...
314 views

### How to sum over half integers? [closed]

I have an expression of the form Sum[1 + x^n + x^(n^2/2), {n, 0, 10}] but I want to sum over half integers, that is, I require that $n \in \mathbb{Z}+\frac{1}{2}$ ...
68 views

### How to condense many FindSequenceFunctions into a single one?

I have a function $f(n,k)$ that is rather large and complex, but if I hold $k$ constant and feed values into Mathematica over many $n$, I can get a closed-form expression for that $k$. However, I can'...
144 views

### Extend a function defined for integers to a differentiable function of a real variable

Here is a function that calculates the probability of randomly landing on a Fibonacci number not greater than $n$: ...
13 views

### solving for the width of a rectangle

Related to this question: solve for two variables for each n related to Collatz conjecture For n=2002, X and Y 0.9999 to 1.0001, step 0.000001, 20000 iterations, giving this output: https://i....