As of May 31, 2023, we have updated our Code of Conduct.

# Questions tagged [recurrences]

The tag has no usage guidance.

303 questions
Filter by
Sorted by
Tagged with
47 views

### Sequences that sum up to possible generalization of Euler or up/down numbers (A000111)

Let $a(n,m,k)$ be an integer sequence with e.g.f. $$A(x)=\operatorname{exp}\left(x + m\int\int (A(x))^k \, dx \, dx\right)$$ I don't know much about integrals, so here's a concrete example: $a(n,1,3)$...
177 views

349 views

### On H. Cohen's four continued fractions for $\zeta(3), \zeta(5), \zeta(7)$?

After 6 years from this old MO post, I finally find in the literature polynomials of deg-$5$ for the continued fraction of $\zeta(5)$. I. Recurrences involving $\zeta(5)$ In Cohen's 2022 paper, ...
78 views

### Simplification of summation and reverse search

Let $f(n)$ be an arbitrary function such that $f(n)\in\mathbb{Z}$. Let $b(n)$ be an integer sequence such that $$b(2^m(2n+1))=\sum\limits_{k=0}^{m}f(m-k)b(2^kn), b(0)=1$$ Let $s(n,m)$ be an integer ...
525 views

99 views

### Solve the recurrence relation with 2 variables

We have the following recurrence relation: \begin{equation} f(n,m) = f(n-1,m) g_{\alpha, \gamma}(n,m) + f(n,m-1) g_{\beta, \gamma}(n,m) \\ g_{\alpha, \gamma}(n,m)= \sum^{n}_{i = 0} \sum^{m}_{j = 0} \...
38 views

228 views

1 vote
49 views

189 views

1 vote
31 views

112 views

89 views

### Recurrence for the number of steps required to get one ball in each box

Given $n$ balls, all of which are initially in the first of $n$ numbered boxes, $a(n)$ is the number of steps required to get one ball in each box when a step consists of moving to the next box every ...
124 views

### How many steps does this subtractive recurrence take?

Given $\alpha\in(0,1)$ and $c\geq1$. $n$ here is in naturals $\mathbb N$. $$T_0=n$$ $$T_i=T_{i-1}-\frac{\lfloor{T_{i-1}}^\alpha\rfloor}c\mbox{ at every }i\in\mathbb N$$ is the recursion. At what $i$ ...
1 vote
99 views

### Number of steps required to get one ball in each box for $n=2^k$

Given $n$ balls, all of which are initially in the first of $n$ numbered boxes, $a(n)$ is the number of steps required to get one ball in each box when a step consists of moving to the next box every ...
358 views