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Recent questions tagged generatingfunctions
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ACE Test Series: Generating Function
The generating function of the sequence $\left \{ a_{0},a_{1},a_{2}..........a_{n}………...\infty \right \}$ where $a_{n}=\left ( n+2 \right )\left ( n+1 \right ).3^{n}$ is $a)3\left ( 1+3x \right )^{2}$ $b)3\left ( 13x \right )^{2}$ $c)2\left ( 1+3x \right )^{3}$ $d)2\left ( 13x \right )^{3}$
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Mar 8
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srestha
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Rosen 7e, Advance Counting techniques , Question 6.f
Find the generating function for the sequence $\left \{ a_n \right \} where $ $a_n = \Large \binom{10}{n+1} $ ... $\Large \color{red}{ \frac{( 1+x )^{10}  1}{x} }$ Please verify
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Mar 7
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Mk Utkarsh
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kennethrosen
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generating function
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Jan 15
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Combinatory
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Rahul_Rathod_
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generatingfunctions
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4
MadeEasy Full Length Test 2019: Combinatory  Generating Functions
Let We define Then ar is equal to. $\binom{r}{2019}$ $\binom{r}{r + 2018}$ $\binom{r}{2019  r}$ $\binom{r}{r  2018}$ Can anyone tell me if this type of question is in Gate 2019 syllabus or ... question in previous year question? If yes, then when can I learn this stuff from. Because I am unable to understand the whole solution.
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Jan 13
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Combinatory
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jhaanuj2108
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madeeasytestseries2019
madeeasytestseries
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Kenneth Rosen Edition 6th Exercise 7.4 Question 7,8 (Page No. 496)
For each of these generating functions, provide a closed formula for the sequence it determines. $a) (3x − 4)^{3}$ $b) (x^{3} + 1)^{3}$
asked
Dec 29, 2018
in
Mathematical Logic
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Sandy Sharma
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1.4k
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80
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discretemathematics
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2
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6
MadeEasy Test Series 2019: Combinatory Generating Functions
Let $M(x) = \frac{x^{2018}}{(1x)^{2019}}$ we define $M(x) = \sum_{r=0}^{\infty}a_{r}x^{r}$ ,then $a_{r}$ is equal to $A)\binom{r}{2019}$ $B)\binom{r}{r+2018}$ $C)\binom{r}{2019r}$ $D)\binom{r}{r2018}$
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Dec 15, 2018
in
Combinatory
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register_user_19
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241
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madeeasytestseries2019
madeeasytestseries
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7
Generating functions
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 __________ .
asked
Dec 12, 2018
in
Mathematical Logic
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shraddha priya
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3.7k
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56
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generatingfunctions
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8
SELF DOUBT GENERATING FUNCTION
Difference between getting closed form of generating function and closed form of the given sequence ,pls someone explain with an example
asked
Dec 10, 2018
in
Combinatory
by
codingo1234
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687
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38
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generatingfunctions
recurrence
0
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0
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9
Kenneth_Rosen_GF
Find a closed form for the exponential generating function for the sequence $\{a_n\}$ where $a_n=\frac{1}{(n+1)(n+2)}$ I broke it down into partial fractions and got $a_n=\frac{1}{n+1}\frac{1}{n+2}$ ... $\sum_{n=0}^{\infty}\frac{1}{(n+2)}.\frac{x^n}{n!}$
asked
Dec 4, 2018
in
Combinatory
by
Ayush Upadhyaya
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52
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generatingfunctions
+2
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0
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10
Kenneth Rosen Edition 6th Exercise 6.4 Question 13 (Page No. 440)
Use Generating function to determine,the number of different ways $10$ identical balloons can be given to four children if each child receives atleast $2$ ballons? Ans given $(x^{2}+x^{3}+.........................)^{4}$ But as there is a upper ... Which one is correct? plz confirm
asked
Dec 4, 2018
in
Combinatory
by
srestha
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110k
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158
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kennethrosen
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11
Generating function(Find Coefficient of x^100)
How to find coefficient of $x^{100}$? $ = (1+x^{10}+(x^{10})^2 + \dots)(1+x^{20}+(x^{20})^2 + \dots)(1+x^{50}+(x^{50})^2 + \dots)\\ = (\frac{1}{1x^{10}}).(\frac{1}{1x^{20}}).(\frac{1}{1x^{50}}) $
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Dec 3, 2018
in
Combinatory
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!KARAN
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114
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generatingfunctions
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3
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12
Generating Function
What will be solution of this function for coefficient of $x^{100}$? $\frac{1}{\left ( 1x^{10} \right )(1x^{20})(1x^{50})}$
asked
Dec 3, 2018
in
Combinatory
by
srestha
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110k
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264
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generatingfunctions
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13
GENERATING FUNCTIONS
asked
Oct 26, 2018
in
Combinatory
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Balaji Jegan
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generatingfunctions
0
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0
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14
General Doubt on Generating Functions
Given only a Generating Function in closed form can we find the sequence it represents? If so, how? Please explain with an example.If not, given a GF(closed form) in general what information does it convey to us about a series if the series is not provided ?
asked
Oct 16, 2018
in
Combinatory
by
tonystark
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167
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42
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generatingfunctions
discretemathematics
kennethrosen
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#counting
+1
vote
1
answer
15
Kenneth Rosen Edition 6th Exercise 7.4 Question 4g (Page No. 496)
Find a closed form of the generating function of the following sequence $0, 1, 2, 4, 8, 16, 32,64,.....$
asked
Oct 14, 2018
in
Combinatory
by
Mk Utkarsh
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34.8k
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98
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generatingfunctions
kennethrosen
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0
votes
1
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16
Kenneth Rosen Edition 6th Exercise 7.4 Question 3e (Page No. 496)
Find closed form for the generating function of the following sequence $\binom{7}{0}, \binom{7}{1}, \binom{7}{2}, ......., \binom{7}{7},0,0,0,0,0,...$
asked
Oct 13, 2018
in
Combinatory
by
Mk Utkarsh
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101
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generatingfunctions
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kennethrosen
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vote
1
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17
Self doubt #Generating functions
$\sum_{.}^{.} (3r^{2} + 5r 21) x^{r}$will be equal to :?
asked
Oct 8, 2018
in
Combinatory
by
Priyanka17
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1.3k
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generatingfunctions
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1
answer
18
Kenneth Rosen Edition 6th Exercise 7.4 Question 6 (Page No. 496)
Find the closed form for the generating function for the sequence $\{a_n\}$ where (a)$a_n=\binom{n}{2}$ for $n=0,1,2....$ (b)$a_n=\binom{10}{n+1}$ for $n=0,1,2....$
asked
Sep 27, 2018
in
Combinatory
by
Ayush Upadhyaya
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25.3k
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116
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kennethrosen
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discretemathematics
0
votes
1
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19
Kenneth Rosen Edition 6th Exercise 6.4 Question 10 (Page No. 440)
Find the coefficient of x^9 in the power series of each of these functions. a) (x3+x5+x6).(x3+x4).(x+x2+x3+x4+⋯) b) (1+x+x^2)^3
asked
Sep 26, 2018
in
Combinatory
by
Na462
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148
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generatingfunctions
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kennethrosen
permutationsandcombinations
+2
votes
2
answers
20
Kenneth Rosen Edition 6th Exercise 6.4 Question 7g (Page No. 440)
Please tell me the approach of solving the question for finding a closed formula for the given generating function: $x^{2} / (1x)^{2}$ . Please determine the general approach how to solve
asked
Sep 25, 2018
in
Combinatory
by
Na462
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8.7k
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156
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generatingfunctions
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kennethrosen
+1
vote
2
answers
21
Rolling of a dice
The number of ways to roll 5 six sided dice to get sum of 25 is ________. _________________________________________________________ if solving with generating function, then why dividing by $\left ( 1x \right )$ if equation is $\frac{x\left ( 1x^{6} \right )}{\left ( 1x \right )}$?
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Aug 23, 2018
in
Combinatory
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srestha
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110k
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201
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generatingfunctions
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1
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22
Kenneth Rosen Edition 6th Exercise 6.4 Example 15 (Page No. 435 )
How to find the coefficient ( for eg $x^7$ ) in the generating function$(1+x+x^2+x^3+..)(1+x^2+x^4+x^6+..)(1+x^5+x^{10}+x^{15}+..)$ ?
asked
Aug 15, 2018
in
Combinatory
by
anip
(
33
points)

93
views
kennethrosen
generatingfunctions
discretemathematics
#counting
+1
vote
0
answers
23
Generating Function Where to start?
Hello can anyone suggest good video/book to learn generating functions from?..i tried the nptel lecture..it has some audio lag. and i could not make much out of it..I am well versed in combinatorics but my calculus is weak.. Please suggest some resource that teaches generating functions from scratch
asked
Jul 19, 2018
in
Combinatory
by
Tridhara Chakrabarti
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407
points)

181
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generatingfunctions
preparation
0
votes
1
answer
24
Kenneth Rosen Edition 6th Exercise 6.4 Question 47 e (Page No. 443)
Find the sequence with each of these functions as its exponential generating function g(x) = $e^{2x}  \frac{1}{1x}$ ... , according to rosen's answer $a_0$ should exist but in my answer $a_0$ is 0. Please let me know where I am missing something.
asked
Jun 26, 2018
in
Combinatory
by
Ayush Upadhyaya
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160
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kennethrosen
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0
votes
1
answer
25
Kenneth Rosen Edition 6th Exercise 6.4 Question 46 e (Page No. 443)
Find a closed form for the exponential generating function for the sequence $\{ a_n \}$ where $a_n=\frac{1}{n+1}$ and the exponential generating function for the sequence $\{a_n\}$ is the series $\sum_{n=0}^{\infty}\frac{a_n}{n!}x^n$
asked
Jun 26, 2018
in
Combinatory
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Ayush Upadhyaya
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143
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kennethrosen
+1
vote
1
answer
26
Kenneth Rosen Edition 6th Exercise 6.4 Question 8 c (Page No. 440)
1/1−2x2 provide close formula for the sequences it determines
asked
Jun 14, 2018
in
Combinatory
by
sunil sarode
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1.5k
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75
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generatingfunctions
kennethrosen
discretemathematics
+3
votes
1
answer
27
Kenneth Rosen Edition 6th Exercise 6.4 Question 6 e (Page No. 440)
nC2 for n=0,1,2,3...
asked
Jun 14, 2018
in
Mathematical Logic
by
sunil sarode
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1.5k
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128
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kennethrosen
discretemathematics
counting
generatingfunctions
0
votes
1
answer
28
Combinatorics
Find the number of seven digit integers with sum of the digits equal to $11$ and formed by using the digits $1,2$ and $3$ only. Soln $X_{1}+X_{2}+.......X_{7}=11$ $(x+x^{2}+x^{3})^{7}$ $(x(1+x+x^{2}))^{7}$ $x^{7}(1+x+x^{2})^{7}$ ... (7k) (x)3k) * ((7+k1k) xk) $((\binom{7}{k}) (x)^{3k}) \times (\binom{7+k1}{k} x^{k})$ Now not able to proceed. Kindly help.
asked
May 23, 2018
in
Combinatory
by
mbisht
(
275
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81
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engineeringmathematics
generatingfunctions
discretemathematics
counting
+2
votes
4
answers
29
kennneth rosen chapter counting
1. Find the coefficient of $x^{10}$ in the power series. $\left ( 1+x^{2}+x^{4}+x^{6}+x^{8}+.... \right )\left ( 1+x^{4}+x^{8}+x^{12}+.... \right )\left ( 1+x^{6}+x^{12}+x^{18}+.... \right )$ ... ........now not able to proceed. 2.Provide a closed formula for the sequence it determines x2+3x+7+(1/(1x2))
asked
May 18, 2018
in
Combinatory
by
mbisht
(
275
points)

210
views
generatingfunctions
+1
vote
2
answers
30
Generating Function
Find $\left [ x^{50} \right ]$ $\left ( x^{6}+x^{7}+x^{8}+.... \right )^{6}$
asked
May 18, 2018
in
Combinatory
by
Nils
Junior
(
917
points)

135
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generatingfunctions
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