# Questions tagged [recurrences]

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### Explicit expression for recursive sums - II

A twist on just unfolded recursive summation formula. Let polynomials in nonnegative integer variables $t_1,t_2,\dots$ be defined by the recurrence: \begin{split} g_0 &= 1, \\ g_k(t_1,t_2,\dots,...
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### Explicit expression for recursive sums

Let $t_1,t_2,\dots,t_k$ be non-negative integers. Can the following sum $$f_k(t_1,t_2,\dots,t_k):=\sum_{j_1=0}^{t_1} \sum_{j_2=0}^{t_2+j_1} \sum_{j_3=0}^{t_2+j_2} \dots \sum_{j_k=0}^{t_k+j_{k-1}} 1$$ ...
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### Asymptotics of holonomic recurrences and the Birkhoff-Trjitzinsky method

While reading about asymptotics of holonomic recurrences, I had the following impressions that are related to the divulgation of the theory: I don't know what is the current status of the divulgation ...
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### Reference request: Counting integer sequences in homogeneous linear recurrences

Are there references in the literature that deal with the probability of finding an integer sequence in a linear homogeneous recurrence with constant coefficients $\in \mathbb{Z}$? (or provides a way ...
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### Bounding the $n$-th term of a sequence, given a non-linear recursive bound
I asked the following question in MSE: Let $a,b\in\mathbb{R}^+$. Suppose that $\{x_n\}_{n=0}^\infty$ is a sequence satisfying $$|x_n|\leq a|x_{n-1}|+b|x_{n-1}|^2,$$ for all $n\in\mathbb{N}$. How can ...