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$a_1=1,a_{n+1}=\frac{n}{a_n}+\frac{a_n}{n}$. Prove that for $n\ge4$, $\lfloor{a_n^2}\rfloor=n$

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#sequences-and-series #elementary-number-theory #recurrence-relations #contest-math #ceiling-and-floor-functions
823
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Recurrence sequence limit

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#calculus #sequences-and-series #limits #recurrence-relations #induction
77
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Find a closed form solution of the recurrence f(a, b) = f(a, b-1) + f(a-1, b-1) with base cases f(0, 0) = 1, f(k, 0) = 1, f(0, k) = 0 (k>0).

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#discrete-mathematics #recurrence-relations
4.9k
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Find and solve a recurrence relation for the number of n-digit ternary sequences with no consecutive digits being equal

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#combinatorics #recurrence-relations
70
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How to solve this recurrence?

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#recurrence-relations
131
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recurrence relation

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#discrete-mathematics #recurrence-relations
176
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Argument over an induction proof

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#proof-verification #proof-writing #induction #recurrence-relations #recreational-mathematics
4.3k
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Combinatorics - Recurrence relation with n letter sequences

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#combinatorics #recurrence-relations
111
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How to solve this specific recurrence relation

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#recurrence-relations
83
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Limit of a recursively defined sequence

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#analysis #recurrence-relations
799
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number of derangements

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#combinatorics #algorithms #recurrence-relations #permutations #recursive-algorithms
1.2k
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Number of ways to arrange n identical stones into piles

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#combinatorics #recurrence-relations #recursive-algorithms
3.7k
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Combinatorics - Catalan numbers recursive function proof by induction help

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#combinatorics #recurrence-relations #induction #catalan-numbers
2.4k
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Combinatorics recurrence relation - n digit ternary sequences (non homogenous)

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#combinatorics #recurrence-relations
36
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Probability, that when we send a $0$ down the network we will get back a $0$

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#discrete-mathematics #recurrence-relations

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