List questions from recurrence-relations

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binary n-length sequences without 011

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How to find the closed form formula of this sequence

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Number of permutation such that $\sigma (k) \ne k-1$

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Convergence of the recursive sequence $x_n=\frac{x_{n-1}}2+\frac3{x_{n-1}},n\ge 1$

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Closed form for terms of two linked sequences, existence of limiting values?

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Find solutions of recursive equations

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For $n\in\Bbb{N}$, count the number of permutations $\pi$ such that $|i-j|\leq 1$ implies that $|\pi(i)-\pi(j)|\leq 2$

Published on 16 May 2020 - 14:54

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If $S_n=\sum _{i=1}^n\frac{1}{a_i}$ and $a_k=\left(\prod _{i=1}^{k-1}a_i\right)+1$ then evaluate $\lim _{n\to \infty }S_n$.

Published on 28 Mar 2026 - 22:29

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Solving recurrence relation with initial conditions given

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Determinant of the square matrix $A$ where $a_{i,j}=|j-i|$

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Using backtracking to convert from recursive to explicit formula

Published on 30 Mar 2026 - 9:44

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Laisant’s recurrence relation

Published on 23 Feb 2026 - 8:34

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Show that $z_{k-1}z_{k+1}=z_k+1 \rightarrow z_5=\frac{z_1+1}{z_2}$

Published on 19 May 2020 - 16:53

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Recurrence relation with derivatives

Published on 25 Mar 2026 - 16:06

List Question

Concrete Mathematics 1.16

binary n-length sequences without 011

How to find the closed form formula of this sequence

Number of permutation such that $\sigma (k) \ne k-1$

Convergence of the recursive sequence $x_n=\frac{x_{n-1}}2+\frac3{x_{n-1}},n\ge 1$

Closed form for terms of two linked sequences, existence of limiting values?

Find solutions of recursive equations

For $n\in\Bbb{N}$, count the number of permutations $\pi$ such that $|i-j|\leq 1$ implies that $|\pi(i)-\pi(j)|\leq 2$

If $S_n=\sum _{i=1}^n\frac{1}{a_i}$ and $a_k=\left(\prod _{i=1}^{k-1}a_i\right)+1$ then evaluate $\lim _{n\to \infty }S_n$.

Solving recurrence relation with initial conditions given

Determinant of the square matrix $A$ where $a_{i,j}=|j-i|$

Using backtracking to convert from recursive to explicit formula

Laisant’s recurrence relation

Show that $z_{k-1}z_{k+1}=z_k+1 \rightarrow z_5=\frac{z_1+1}{z_2}$

Recurrence relation with derivatives

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