#ATTENDANCE QUIZ FOR LECTURE 19 of Dr. Z.'s Math454(02) Rutgers University


# Please Edit this .txt page with Answers


#Email  ShaloshBEkhad@gmail.com 
#Subject: p19
#with an attachment called
#p19FirstLast.txt
#(e.g. p19DoronZeilberger.txt)


#Right after finishing watching the lecture but no later than Nov. 13, 2020, 8:00pm




THE NUMBER OF ATTENDANCE QUESTIONS WERE:


PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH, BY THE ANSWER


1. (i) What is the explicit expression for the sequence 


a(0) = 0, a(1) = 0, a(2) = 0, a(n) =1 for n=3,4……
f(x) = 


(ii) Use maple to find explicit expression for generating function for the sequence 0,1,8,27,64, 125 
 x*(1+4*x+x^2)/(1-x)^4


(iii) 1,n binomial (n,2),...,binomial(n,n) 


2. Find the EGF of a(n)=n for 0<=n<=5, a(n)=0 if n>=6 
a(0) = 0, a(1) = 1, a(2) =2, a(3) =3, a(4) =4, a(5) =5
0+1x+1x^2+½x^3+1/4x^4 + 5/70x^5


3. What is the EFS of a(n) =0 for n=0,1,2,3,4,5 and a(n)=1 for n>=6
a(0) ---> a(5)=1
a(5) …. a(n) = 1 


1x^5 + 1x^6 +½ x^7 +...


4. Find the EGF of a(0) =0, a(1) =0, a(n)=(n-1)! For n>=2 


5. (i) What is the A number? A001187
(ii) How many digits does the number of labeled connected graphs within 150 vertices have?
For j >= 2, Vol(C_j ) is equal to the number of labeled connected graphs on j - 1 vertices.
6. Use the technique of weight enumeration to find the exact number of sequences a[1],a[2],....a[r] where each of the a[i] is a number of {3,4,7} that add up to 1001. 
7. Is [{{1,3,4},{6,7}}, 52] a member of x(7)? Why?
8. How many trees of the form [labeled tree, permutation, SetPartition] of size 150 (meaning that the number of vertices of the tree & the length of the permutation + the size of the set that SetPartition is 150?