# Tagged Questions

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### Comparing Generalized Continued Fractions

Gosper lays out a method (under Approximations) for comparing regular (a.k.a simple) continued fractions which have all partial numerators set to 1. Continue comparing terms until they differ, then ...
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### Produce a list of the most-similar units, given various correlations/relationships

I have a database full of units (U1 - U50, U51...) where every unit has the same standard attributes (A1 - A10) and where a % of each attribute defines the amount of that attribute for that particular ...
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### Limit of a recursiv trigonometric function

So while doing my math homework I recently stumbled upon this little thing: It seems that $y_n = \sin(y_{n-1}) + k$ with arbitrary $y_0$ and $k$ converges to a definite value for $n \to \infty$. ...
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### Finding the inhomogeneous solution

$x_{n+2} = x_{n+1} + 20x_n + n^2 + 5^n \text{ with } x_0 = 0 \text{ and } x_1 = 0$ How would I find the inhomogeneous solution for this since the homogenous solution is 0 given initial conditions?
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### Towers of Hanoi recurrence relation

How would I do this recurrence relation?
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### Help solving recursive relations

$x_{n+2} = x_{n+1} + 20x_n + n^2 + 5^n \text{ with } x_0 = 0 \text{ and } x_1 = 0$ How would you solve this recursive relation? I have the homogenous solution, but am having issues with the ...
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### recursive relation for putting signs in 2*n table

Consider we have a $2\times n$ table and we want to put a sign in some of the cells, and we don't put signs in both adjacent cells give a recursive phrase that shows that how many ways we can do that? ...
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### N balls of k colors on a cirlce, no two neighboring balls have same color - recursive algorithm

Suppose we have N balls of k different colors. What is the number of arrangements of these N balls on a circle with no two neighboring balls having the same color? Actually, the task is to make up a ...
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### Recursive Function - $f(n)=f(an)+f(bn)+n$

I've got this recursive function $f(n)=f(an)+f(bn)+n$, and I need to find $θ$ on $f(n)$, as $a+b>1$. Using a recursive tree, I managed to bound it by $n\log(n)$ from the bottom and by $n^2$ from ...
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I tried to solve this recurrence relation, but I was confused when I had to determine the pattern. $$T(n) = \begin{cases} 3, & \text{if }n = 0 \\ T(n - 1)^2, & \text{if }n > 0 \end{cases} ... 0answers 61 views ### Solving a Recurrence Relation With Summation and Tau Function How can I solve the following:$$ T(n) = \sum_{i = 1}^{d(n) - 2}T(v_i) + \sum_{i = d(n) - 1}^{n - 1}c + c' $$Where d(n) is the Tau function, and v is the set of values dividing n. e.g. d(18) = ... 0answers 26 views ### Verify that this recurrence relation is in O(log n) For the recurrence T(n)=2*\lceil\frac{n+1}{2}\rceil+c is in \Theta(lg n) My attempt at a solution (mostly just wanting to verify its correct). Lower Bound: T(n)=2*\lceil\frac{n+1}{2}\rceil+c ... 2answers 53 views ### Solving this recurrence relation Hi all I'm preparing for a midterm and the following appeared as a practice problem that I'm not quite sure how to solve. It asks to find a tight bound on the recurrence using induction$$ {\rm ...
I read this on Wolfram Alpha. It states that: a quadratic recurrence relation uses a second degree polynomial to express $x_{n+1}$ as a function of $x_n$. A "quadratic map", then, is a recurrence ...