#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
#Attendance Question 1
#What is the explicit expression for the sequence 
#a(0)=0, a(1)=0, a(2)=0, a(n)=1 for n=3,4,...
#Use maple to find an explicit expression for the generating function
#of 0,1,8,27,64,125, ...,a(n)=n^3
#Attendance Answer
#x*(1+4*x+x^2)/(1-x)^4

#Attendance Question 2
#Find the EGF of a(n)=n for 0<=n<=5 a(n)=0 if n>=6
#Attendance Answer
#a(0)*x/0! +a(1)*x/1!+a(2)*x^2/2! +0*x^3/3!

#Attendance Question 3
#Find the EGF of a(0)=0, a(1)=0, a(n)=(n-2)! for n>=2
#Attendance Answer
#a(0)*x/0! +a(1)*x/1!+a(2)*x^2/2! +0*x^3/3!

#Attendance Question 4
#What is the A-number of this sequence 
#How many digits does the number of labeled connected graphs with 150 vertices has?
#Attendance Answer
#A1187

#Attendance Question 5
#Use the weight enumeration to find the exact number of sequences a[1],a[2],...,a[r]
#Where each of the a[i] is a member of {3,4,7} that add-up to  1001
#Attendance Answer 
#29853

#Attendance Question 6
#Is [{{1,3,4}.{6,7}},52] a member of X(7)?
#Attendance Answer
#Yes

#Attendance Question 7
#Later on we will prove that EGF os labelled trees is 
#1+Sum(n^(n-2)*x^n/n!,n=1..infinity
#How many triples of the form 
#[Labeled tree,Permutation,SetPartition]
#of SIZE 150 (meaning that the number of vertices of the free +the length of 
#the permutation + the size of the set that set partition  partitions is 150
#Attendance Answer
#45846244