List questions from generating-functions

Published on 03 Jun 2020 - 7:34

117

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Ways to fill up a $4 \times 4$ matrix with numbers $1$ to $16$, s.t its rank is $1$ under modulo $17$

Published on 04 Jun 2020 - 4:01

31

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Counting sequences $(c_1,\ldots,c_n)$ of integers $c_i\geq -1$ such that $\sum_{i=1}^n c_i=0$, and for all $1\leq i \leq n$, $\sum_{j=1}^i c_j\geq 0$.

Published on 05 Jun 2020 - 18:35

260

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Counting with Recurrence Relations

Published on 24 Feb 2026 - 3:00

852

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Generating function given the recurrence relation

Published on 06 Jun 2020 - 11:32

63

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Generating function of a Fibonacci series but with certain variation.

Published on 29 Mar 2026 - 4:33

35

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Independence of discrete random variable

Published on 30 Mar 2026 - 5:23

49

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Assign 25 identical items to 8 different people

Published on 07 Jun 2020 - 8:42

114

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Find the coefficient of $x^k$

Published on 25 Mar 2026 - 22:23

43

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Assign the number of ways to share 16 identical objects

Published on 25 Mar 2026 - 22:26

31

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Finding Coefficients via Generating Functions

Published on 07 Jun 2020 - 18:20

72

Views

Counting endofunctions with a certain recurrent condition.

Published on 25 Mar 2026 - 1:14

377

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Binomial Expansion $(1+kx)^4 (1+x)^n$

Published on 08 Jun 2020 - 2:18

131

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Mistake in the proof of Binet's formula

Published on 29 Mar 2026 - 4:34

62

Views

A combinatorial identity

Published on 08 Jun 2020 - 7:23

List Question

Solve $f(0)=0,f(1)=1, \forall n\ge2, f(n)= 2f(n-1)+\frac{(-1)^n}{n!}$ using generating functions

Ways to fill up a $4 \times 4$ matrix with numbers $1$ to $16$, s.t its rank is $1$ under modulo $17$

Counting sequences $(c_1,\ldots,c_n)$ of integers $c_i\geq -1$ such that $\sum_{i=1}^n c_i=0$, and for all $1\leq i \leq n$, $\sum_{j=1}^i c_j\geq 0$.

Counting with Recurrence Relations

Generating function given the recurrence relation

Generating function of a Fibonacci series but with certain variation.

Independence of discrete random variable

Assign 25 identical items to 8 different people

Find the coefficient of $x^k$

Assign the number of ways to share 16 identical objects

Finding Coefficients via Generating Functions

Counting endofunctions with a certain recurrent condition.

Binomial Expansion $(1+kx)^4 (1+x)^n$

Mistake in the proof of Binet's formula

A combinatorial identity

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