Kenneth Chan
#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 problem 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...
(ii)Use Maple to find an explicit expression for the generating function of 
0,1,8,27,64,125...a(n)=n^3
Answer
(i)f(x)=3x+4x
(ii)

Attendance Problem 2
Find the EGF of a(n)=n, for 0<=n<=5, a(n)=0 if n>=6
Answer 
a(0)x/0!+a(1)x/1!+a(2)x/2!+a(3)x/3!+a(4)x/4!+a(5)x/5

Attendance Problem 3
What is the EGF of a(n)=0 for n=0,1,2,3,4,5 and a(n)=1 for n>=6
Answer
0 because the coeffiecents for all n's are 0

Attendance Problem 4
Find the EGF of a(0)=0, a(1)=0, a(n)=(n-2)! for n>=2
Answer
a(n)x/(n-1)!

Attendance Question 
(i)What is the A-number of this sequencve 
(ii) how many digits does the number of labeled connected graphs with 150 verties has?
Answer
(i)A001187
(ii)150!

Attendance Question
Use the Technique of Weight-enumeration to find the exact number of sequences a[1],a[2],...
a[r],(r can be any length)
where each of the a[i] is a member of {3,4,7} that add up to 1001
(i)less than 400?

Attendance Question
(i) is ({{1,3,4},{6,7}},52 a member of X(7)?
Why
Answer
no because it is based off of combinatorial family and it would be the  same sequence 
as the one recorded earlier

Attendance Question 
How many Triples of the form [Labeled Tree, Permutation, SetPartion]
of Size 150 (meaning that the number of vertices of the tree+ the length of the Permutation + the size of the set that setpartitions is 150
Answer
1/3?