List questions from recurrence-relations

Published on 25 Mar 2026 - 11:18

335

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Conjecture: If $a_1\in\mathbb{Z}$ and $a_n=\sec (a_{n-1})$ then the proportion of positive terms approaches $\frac{1}{\sqrt{2\pi}}$ as $n\to\infty$.

Published on 15 Apr 2026 - 12:27

315

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For the following recurrence, sketch its recursion tree, and guess a good asymptotic upper bound on its solution.

Published on 13 Apr 2026 - 17:34

112

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Number of subsets $\{1, 2, \dots, n\}$ without numbers with forbidden differences.

Published on 14 Apr 2026 - 2:00

102

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Show that $x_{n+1} = \frac{2x_n}{\sqrt{1+2^{-n}x_n}+1}$ is monotone and bounded

Published on 14 Apr 2026 - 17:00

571

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Finding a formula for the sequence $ 2, 4, 10, 28, 82, \dots $

Published on 16 Apr 2026 - 12:18

47

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Reference for iteration of vector fields on Riemannian manifolds.

Published on 21 Apr 2026 - 15:57

43

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Three term recurrence relation with two indices and variable coefficients

Published on 11 Apr 2026 - 18:40

21

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Gambler's ruin expected mean time of absorption

Published on 11 Apr 2026 - 11:17

109

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Asymptotics of $f(n)=\frac{2}{n}\sum_{i=1}^{n-2}f(i) + 1$

Published on 17 Apr 2026 - 2:32

75

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Sum over recursive sequence with non-constant coefficients

Published on 12 Apr 2026 - 11:24

47

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How to solve a recursion to find a closed form solution?

Published on 11 Apr 2026 - 10:33

84

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Nonlinear recurrence equation solution

Published on 10 Apr 2026 - 7:16

64

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Branching factor of a pathfinding procedure

Published on 13 Apr 2026 - 19:11

160

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how to find the formula for $n$-th Fibonacci numbers ($F_n = \frac{a^n-b^n}{a-b}$) and prove it without induction.

Published on 16 Apr 2026 - 6:47

List Question

Big-O analysis of recurrence relation

Conjecture: If $a_1\in\mathbb{Z}$ and $a_n=\sec (a_{n-1})$ then the proportion of positive terms approaches $\frac{1}{\sqrt{2\pi}}$ as $n\to\infty$.

For the following recurrence, sketch its recursion tree, and guess a good asymptotic upper bound on its solution.

Number of subsets $\{1, 2, \dots, n\}$ without numbers with forbidden differences.

Show that $x_{n+1} = \frac{2x_n}{\sqrt{1+2^{-n}x_n}+1}$ is monotone and bounded

Finding a formula for the sequence $ 2, 4, 10, 28, 82, \dots $

Reference for iteration of vector fields on Riemannian manifolds.

Three term recurrence relation with two indices and variable coefficients

Gambler's ruin expected mean time of absorption

Asymptotics of $f(n)=\frac{2}{n}\sum_{i=1}^{n-2}f(i) + 1$

Sum over recursive sequence with non-constant coefficients

How to solve a recursion to find a closed form solution?

Nonlinear recurrence equation solution

Branching factor of a pathfinding procedure

how to find the formula for $n$-th Fibonacci numbers ($F_n = \frac{a^n-b^n}{a-b}$) and prove it without induction.

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