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Generating-functions
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How to find closed-form expression of this series?
July 23rd, 2022
closed-form
combinatorics
generating-functions
Determine the number of all nonnegative integer solutions to $x + y + z = 11$ with $x\leq 3$, $y\leq 4$, and $z \leq 6$.
July 31st, 2022
generating-functions
Using generation functions solve the following difference equation
August 20th, 2022
generating-functions
recurrence-relations
discrete-mathematics
General term for fibonacci sequence
October 20th, 2020
generating-functions
fibonacci-numbers
linear-algebra
algebra-precalculus
Generating Functions of Binary Strings
November 14th, 2020
generating-functions
discrete-mathematics
Dice rolls-Generating Functions
June 14th, 2020
combinatorics
generating-functions
Find a closed form for the generating function for each of these sequences
August 1st, 2022
generating-functions
discrete-mathematics
Closed form for nth term of generating function
August 1st, 2022
closed-form
combinatorics
generating-functions
Generating function of trigonometric fuction
February 17th, 2020
trigonometry
generating-functions
Use generating functions to prove Pascal’s identity
August 1st, 2022
discrete-mathematics
generating-functions
Find coefficient of $X^{12}$
June 21st, 2020
generating-functions
combinatorics
discrete-mathematics
recurrence-relations
Find a closed form of the generating function for $a(n) =3n^2+4n+5$, $n=0,1,2,....$
May 12th, 2020
generating-functions
Generating function - the number of ways to distribute 100 dollars to n people.
January 30th, 2020
generating-functions
Find a recurrence relation and associated generating function for the number of different binary trees with n leaves
April 22nd, 2020
catalan-numbers
generating-functions
recurrence-relations
combinatorics
$P(x)=\sum_{n=0}^{\infty} p_nx^n=1+x+2x^2+3x^3+5x^4+7x^5+11x^6+\cdots$ and $Q(x)=\sum_{n=0}^{\infty} q_nx^n.$ What is $\dfrac{Q(x)}{P(x)}$?
November 9th, 2020
integer-partitions
functions
generating-functions
combinatorics
Find generating functions given a sequence, and vice versa?
August 1st, 2022
power-series
combinatorics
discrete-mathematics
binomial-coefficients
generating-functions
How to determine the probability given the PGF?
October 8th, 2020
generating-functions
probability-theory
Moment generating function, change of variable
August 1st, 2022
probability
generating-functions
Convert a closed-form generating function to a sequence
August 1st, 2022
generating-functions
Find the generating function for the finite sequence 0,0,0,1,2,3,4,5
August 1st, 2022
generating-functions
combinatorics
Generating function. Inverse.
August 1st, 2022
generating-functions
Derive recurrence relation for Chebyshev polynomials from generating function
December 3rd, 2020
generating-functions
recurrence-relations
chebyshev-polynomials
How many solutions possible for the equation ${2x}+{3y}+{7z}={r}$
August 1st, 2022
generating-functions
discrete-mathematics
combinatorics
Evaluate the following sums using generating functions
April 6th, 2020
generating-functions
summation
combinatorics
sequences-and-series
exponential generating functions containing an even/odd number of cycles
April 29th, 2021
generating-functions
combinatorics
exponential generating function for distinct objects into distinct boxes
November 7th, 2020
generating-functions
combinatorics
Recurrence relation for the number of strings of length $n$ in base $3$
December 29th, 2020
discrete-mathematics
recurrence-relations
generating-functions
Combinatorics: Binary Strings
June 20th, 2020
binary
combinatorics
generating-functions
Circular permutations with alike objects
August 1st, 2022
generating-functions
binomial-coefficients
discrete-mathematics
combinatorics
Multiple choice question about generating function of a sequence
June 21st, 2020
generating-functions
analysis
sequences-and-series
calculus
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