List questions from recurrence-relations

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Why does $T(n) \leq 2 T(\lceil \frac{n}{2} \rceil)+\mathcal{O}(n)$ imply $T(n)=\mathcal{O} (n\log(n))$

Published on 28 Mar 2026 - 15:36

3.6k

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The number of length-n ternary sequences with even ones and even zeroes

Published on 01 May 2014 - 3:07

87

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Given initial conditions and a recurrence relation, what is closed form in terms of n?

Published on 01 May 2014 - 5:00

3.7k

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Find an explicit formula for the recursive sequence

Published on 27 Mar 2026 - 23:22

135

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third order recurrence relation with non-constant coefficients

Published on 01 May 2014 - 16:27

223

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Fibonacci polynomials and factorization redux

Published on 01 May 2014 - 18:38

1.7k

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Solving recurrence relation: $ f(n) = 3f(n/2) - 2f(n/4) | f(2) = 5, f(1) = 3$

Published on 29 Mar 2026 - 2:37

1.3k

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Finding an explicit formula for $a_n$ defined recursively by

Published on 30 Mar 2026 - 6:09

389

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Recurrence Relation all general solutions

Published on 03 May 2014 - 18:21

481

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Solving divide and conquer recurrence

Published on 03 May 2014 - 19:41

179

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Recursive Function - $f(n)=f(an)+f(bn)+n$

Published on 26 Mar 2026 - 6:05

730

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For $x_{n+1}=x_n^2-2$, show $\lim_{n\to\infty}\frac{x_n}{x_0x_1\cdots x_{n-1}}=2$

Published on 04 May 2014 - 16:18

49

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Find general solution

Published on 05 May 2014 - 15:01

98

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Zeroes of polynomial

Published on 05 May 2014 - 17:20

180

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A non-homogenous linear recurrence: Why does my method fail?

Published on 06 May 2014 - 0:18

List Question

Why does $T(n) \leq 2 T(\lceil \frac{n}{2} \rceil)+\mathcal{O}(n)$ imply $T(n)=\mathcal{O} (n\log(n))$

The number of length-n ternary sequences with even ones and even zeroes

Given initial conditions and a recurrence relation, what is closed form in terms of n?

Find an explicit formula for the recursive sequence

third order recurrence relation with non-constant coefficients

Fibonacci polynomials and factorization redux

Solving recurrence relation: $ f(n) = 3f(n/2) - 2f(n/4) | f(2) = 5, f(1) = 3$

Finding an explicit formula for $a_n$ defined recursively by

Recurrence Relation all general solutions

Solving divide and conquer recurrence

Recursive Function - $f(n)=f(an)+f(bn)+n$

For $x_{n+1}=x_n^2-2$, show $\lim_{n\to\infty}\frac{x_n}{x_0x_1\cdots x_{n-1}}=2$

Find general solution

Zeroes of polynomial

A non-homogenous linear recurrence: Why does my method fail?

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