-2
votes
1answer
26 views

Closed form questions [on hold]

Please could you help me to find the generating functions of the following sequences in closed form: (a) 1, 0, 1, 0, 1, 0, … (b) 2, –4, 6, –8, 10, –12, …
0
votes
1answer
38 views

The closed form of a sum of mod(k,m) where k goes from 1 to a arbitrary number.

Is there a closed form for $\sum_{n=0}^{C} mod(n,m)$ for arbitrary integers m ?
0
votes
3answers
88 views

How to solve a recursive equation

I have been given a task to solve the following recursive equation \begin{align*} a_1&=-2\\ a_2&= 12\\ a_n&= -4a_n{}_-{}_1-4a_n{}_-{}_2, \quad n \geq 3. \end{align*} Should I start by ...
2
votes
4answers
425 views

How to find a closed form solution to a recurrence of the following form?

I need to find the closed form solution to the following recurrence -: $ T(n) = 8*T(n/2) + 0.25*n^2$ with $T(1) = 1$ and $n=2^j$ and this is what I have tried so far but just can't seem to get a ...
1
vote
1answer
100 views

Recursive and closed form solution for choosing $n$ pairs/triplets.. of $kn$ elements.

I stumbled apon an interesting question: How many ways are there to arrenge $kn$ elements into $n$ sets, $k$ elements each? There should be a recursive and closed form solution for $g_k(n)$. For ...
2
votes
1answer
230 views

Recurrence relation for $n$ numbers in which no 3 consecutive digits are the same.

I am stuck on trying to find (and solve) a recurrence relation to find all n-digit numbers in which no 3 consecutive digits are the same. These numbers are in decimal expansion. Now I first ...
3
votes
1answer
227 views

Finding a Linear Recurrence Relation

A model for the number of lobsters caught per year is based on the assumption that the number of lobsters caught in a year is the average of the number caught in the two previous years. ...
0
votes
4answers
293 views

Having a lot of trouble solving this recurrence with iteration and finding a closed form…

I'm learning discrete math and didn't have any trouble with any recurrences in the examples I went over through the chapters on it, but this one problem at the end of the first chapter is killing me, ...
2
votes
0answers
146 views

Can this series be expressed in closed form, and if so, what is it?

Can this series be expressed in closed form, and if so, what is it? $$ \sum_{n=1}^\infty\frac{1}{9^{n+1}-1} $$
2
votes
2answers
282 views

Closed-form Expression for $\sum_{j=0}^{k-1}(2j+2)\sum_{i=1}^j \frac 1 {i^2}$? (problem with Mathematica)

I need to calculate a closed-form expression for $\sum_{j=0}^{k-1}(2j+2)\sum_{i=1}^j \frac 1 {i^2}$. This isn't particularly difficult, and I do it by hand pretty much routinely. However I found out ...