#ATTENDANCE QUIZ FOR LECTURE 21 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p21
#with an attachment called
#p21FirstLast.txt
#(e.g. p21DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Nov. 20, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 4

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




Question 1:

How many connected graphs are there with 30 vertices and 50 edges?


Answer 1:

L:=WtEdConGclever(30,a):

coeff(L[30],a,50)
 
616531513027177775473601317524937092680978914590598004251998471840




Question 2:

Find the number of labelled graphs with 50 vertices and 5 components.


Answer 2:

NuKcomp(50,5)[50]

84788987690871322213720759813193437723400498985997782717718839577530578491639411074799027505529978132256881827900900288575885348212857384767830040557053247256490676318714477784265805319979127545883387577706020661320917668889000205517435779132191852077004426477271855375638163003674948760253727467070410930283337482240



Question 3:

How many labelled connected graphs are there with 30 vertices and 50 edges?


Answer 3:

L:=WtEdConGclever(30,a):

coeff(L[30],a,50)

616531513027177775473601317524937092680978914590598004251998471840



Question 4:

For i=2, 3, 4... find the OEIS A number if it exists of NuKcomp(20,i)

What is the smallest I for which it is not in the OEIS?


Answer 4:

i=1 : A001187

i=2 : A323875

i=3 : A323876

i=4 : A323877

i=5 : Not in the OEIS!

The smallest i for which the corresponding sequence is not in the OEIS is i=5.