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Recent questions tagged generating-functions

1 votes
2 answers
63
Generating Function
Find $\left [ x^{50} \right ]$ $\left ( x^{6}+x^{7}+x^{8}+.... \right )^{6}$
Find $\left [ x^{50} \right ]$$\left ( x^{6}+x^{7}+x^{8}+.... \right )^{6}$
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1 votes
1 answer
64
Generating function
1. Find a closed form for the generating function for the sequence $1,1,0,1,1,1,1,1,1,1,...........$ 2. Find a closed form for the generating function for the sequence $a_n= 2n+3$ for all $n=0,1,2,....$
1. Find a closed form for the generating function for the sequence $1,1,0,1,1,1,1,1,1,1,...........$2. Find a closed form for the generating function for the sequence $a_...
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0 votes
1 answer
65
Exponential Generating Function
Is Exponential Generating Functions asked in GATE ?
Is Exponential Generating Functions asked in GATE ?
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1 votes
1 answer
66
Kenneth Rosen Edition 6th Exercise 6.4 Question 33 (Page No. 442)
Use generating function to solve the recurrence relation $a_k=3{a_{k-1}} + 2$ with initial conditions $a_0=1 $.
Use generating function to solve the recurrence relation $a_k=3{a_{k-1}} + 2$ with initial conditions $a_0=1 $.
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0 votes
1 answer
67
Generating functions
In generating function i studied from books i didn't understand two things 1. How to apply generating functions for solving recurrence relation 2. Generating functions for solving Permutations Can anybody explain it with an example ?
In generating function i studied from books i didn't understand two things1. How to apply generating functions for solving recurrence relation2. Generating functions for ...
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2 votes
2 answers
68
Generating functions
What will be the coefficient of x^17 in the expansion of (x+x^2+x^3+x^4+x^5+x^6)^4?
What will be the coefficient of x^17 in the expansion of (x+x^2+x^3+x^4+x^5+x^6)^4?
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1 votes
1 answer
69
Generating function doubt
Please give me clarification
Please give me clarification
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2 votes
0 answers
70
Extended Binomial Coefficients
Find the value of extended Binomial Coefficient $\binom{-1/2}{3}$
Find the value of extended Binomial Coefficient $\binom{-1/2}{3}$
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1 votes
1 answer
71
Generating Function
How to apply this theorem to $\frac{x^{3}}{1-x}$
How to apply this theorem to $\frac{x^{3}}{1-x}$
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0 votes
3 answers
72
Self doubt generating function
Equation: $x+y=10$ and we are asked to find out the number of a non-negative integral solution of this equation.
Equation: $x+y=10$ and we are asked to find out the number of a non-negative integral solution of this equation.
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42 votes
11 answers
73
GATE CSE 2018 | Question: 1
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$?$\frac...
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0 votes
1 answer
74
discrete maths
What is the coefficient of $x^{12}$ in the power series of $\dfrac{x^3}{(1+2x)^2}?$
What is the coefficient of $x^{12}$ in the power series of $\dfrac{x^3}{(1+2x)^2}?$
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3 votes
1 answer
76
solve
In how many ways can we distribute 77 apples and 66 oranges among 44 children so that each child gets at least one apple? solve by generating function along with approach thanks
In how many ways can we distribute 77 apples and 66 oranges among 44 children so that each child gets at least one apple? solve by generating function along with approac...
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2 votes
0 answers
77
solve
There are 4 oranges, 5 apples and 6 mangoes in a basket. In how many ways can a person make a selection when select at least one fruit from each kind? provide approach thanks in advance
There are 4 oranges, 5 apples and 6 mangoes in a basket. In how many ways can a person make a selection when select at least one fruit from each kind? provide approach th...
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4 votes
1 answer
78
solve by generating function along with approach thanks advance
In how many ways 2 alike apple, 3 alike orange and 4 alike mango can be given to 3 children if each child can have 1 or more than 1 fruits.
In how many ways 2 alike apple, 3 alike orange and 4 alike mango can be given to 3 children if each child can have 1 or more than 1 fruits.
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1 votes
0 answers
80
made easy mock test
The number of ways can 10 balls be chosen from an urn containing 10 identical green balls, 5 identical yellow balls, and 3 identical blue balls are __________.
The number of ways can 10 balls be chosen from an urn containing 10 identical green balls, 5 identical yellow balls, and 3 identical blue balls are __________.
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1 votes
1 answer
82
binomial coefficient
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1 votes
0 answers
83
Kenneth Rosen Ex 5.5
How many positive integers less than 1,000,000 have the sum of their digits equal to 19?
How many positive integers less than 1,000,000 have the sum of their digits equal to 19?
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4 votes
1 answer
85
Generating Function
Q.find number of 7 digit number with sum of digits equal to 11 and formed using digits 1 ,2 ,3 Can we do this with help of generating functions.
Q.find number of 7 digit number with sum of digits equal to 11 and formed using digits 1 ,2 ,3 Can we do this with help of generating functions.
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1 votes
0 answers
86
Self_doubt
How to generalize a given sequence using generating function? If there is a given series say : 1,3,4,5,7,8,10.. how to generalize this sequence? @Habib Sir Please answer this doubt and give a general approach.
How to generalize a given sequence using generating function?If there is a given series say :1,3,4,5,7,8,10.. how to generalize this sequence?@Habib Sir Please answer thi...
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1 votes
0 answers
89
generating function
generating function shifted Fibonacci sequence (what we actually do while finding generating function)
generating function shifted Fibonacci sequence (what we actually do while finding generating function)
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