# Tagged Questions

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### Single formula for this sequence [closed]

Consider the following sequence. 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8 We can express this sequence by (an) where an=n/2 when n is even and an=0 when n is odd. Find a single formula for an ...
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### How to get mathematica to show limit of a recurrence sequence?

I want to find the limit of a such a sequence: $f(n+1)=\sqrt{2f(n)-1}, \, f(0)=a, a>1$ How does one do this? Is it possible to have it show the solution algebraically, like it does with ...
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### Tangled up in sequences and recurrence relations

I took a trip through sequences and recurrence relations and I got tangled up since the documentation didn't help much. I'm sure you can. Given a sequence ...
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### FindSequenceFunction for sum of hypergeometric terms

Mathematica's built-in function FindSequenceFunction is quite good at recognizing hypergeometric terms, i.e. terms $c_k$ for which $c_{k+1}/c_k$ is a rational ...
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### Number of sequences with a certain condition

Suppose I have the sequence {2, 4, 6, 8, 10, 12, 14, 16}. How could I calculate the number of tuples so that for every term save the first one, the difference from ...
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### Can you compute more terms in this sequence?

I am trying to identify a sequence related to the von Mangoldt function matrix. Since I believe/conjecture that the columns in the matrix have period lengths as in this sequence b: ...
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### Graphing the sequence {$p_k$} = $\frac{c - a + dp_{k-1}}{b}$ [duplicate]

Graphing the sequence {$p_k$} = $\frac{c - a + dp_{k-1}}{b}$ I need to know how to graph this function where it automatically plugs in the previous term for $p_{k-1}$, the coefficients are of my ...
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### Creating If statements programmatically [duplicate]

I want to write an algorithm that returns a sequence of numbers, starting from a specified point but stopping once a criterion has been reached. For example ...
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### Faster Ways to compute recursive summation

It takes a long time to compute the summation below, and I'd like to know if there are some better ways to compute things faster. I have used $3$ ways to calculate, but they are very unsatisfactory. I ...
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### Matching a list of sequences with common form

I am trying to find a pattern that matches a list of sequences that share a common form. The sequence form is: 1 followed by zero or more nonzero integers, followed by 0. An example list is: ...
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### Limit of sequence

I tried to calculate the following limit $$\lim_{n\to\infty}n\sin(2\pi en!)$$ Mathematica gets ...
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### Problem on Consecutive Sequence Sums that are Squares

Here is a seemingly simple Problem: I have two natural numbers n and m, n < m such that S1:= n +...+ m is a square and also S2:= n +...+ m + (m+1) is a square. Problem a) : Find n and m. You ...
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### Limit[Sum[(2*E*n)^w/(w^(n/2+w)), {w,2,n}],n->Infinity]

I would like to show that the following (and other similar formulae) tends to zero. Limit[Sum[(2*E*n)^w/(w^(n/2+w)), {w,2,n}],n->Infinity] What's the right ...
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### Defining a recursive integral sequence

I have a recursive integral sequence as follows: $$y_0(x)=1+r,$$ $$y_1(x)=-\frac{1}{\Gamma(a)}\int_0^x (x-t)^{a-1} y_0(t) dt,$$ $$\vdots$$ y_n(x)=-\frac{1}{\Gamma(a)}\int_0^x (x-t)^{a-1} y_{n-1}(t) ...
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### How to detect if a sequence of integers is consecutive

I'm not a math-guy really (a programmer actually) and this is my first question. And excuse me if I can not explain my problem good. The problem is I have a sequence of integers and I want to detect ...
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### Sum of first n items in a sequence [closed]

What's a way to sum over the first n items in a sequence, for example the sequence defined by $2^{k-1}\cdot k$ for $k\in\mathbb{Z},k>0$? I do these by hand all the time but am a bit tired of doing ...
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### How to combine DifferenceRoot objects for odd and even-indexed terms

I'm trying to analyze a certain infinite sequence $S$, indexed by positive integers starting from $1$. It can be split into two subsequences: $S^{odd}$ by removing all even-indexed elements and ...
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### Generation function of recurrence sequence

I'm trying to find generation function of recurrence sequence ...
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### Long waiting time for computing a summation

It takes a long time to compute the summation below, and I'd like to know if there are alternative ways to compute things faster. When replacing $15$ by $\infty$, then I should get $3^{1/3}$. I need ...
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### how can I solve integrals including recursion of some sequences of functions

I would like to solve the equations as given below in mathematica. I have written some codes before but I have no idea when there is sub indexing to indicate the series of functions. I will be very ...
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### Match a sequence of integers

I would to match a pattern p1 = 0,0,1,0,0 to the elements in listA. The elements are a boolean sequence that may look like this ...
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### How to define Similarity Rules?

I have a question about Mathematica's SimilarityRules defining (for e.g. SequenceAlignment function). So help centre clearly ...