#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

1. How many connected graphs are there with 30 vertices and 50 edges?
WtEdConGclever(30, a)[30];
coeff(%, a, 50);
 616531513027177775473601317524937092680978914590598004251998471840

2. Find the number of labeled graphs with 50 vertices and 5 connected components.
NuKcomp(50, 5)[50];
 84788987690871322213720759813193437723400498985997782717718839577530578491639411074799027505529978132256881827900900288575885348212857384767830040557053247256490676318714477784265805319979127545883387577706020661320917668889000205517435779132191852077004426477271855375638163003674948760253727467070410930283337482240

3. How many labeled connected graphs are there with 30 vertices and 50 edges?
Same question as 1

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?
NuKcomp(20, 2);
 [0, 1, 3, 19, 230, 5098, 207536, 15891372, 2343580752, 675458276144, 383306076989440, 430041136692146912, 956431386434331323776, 4224539434553753578497024, 37106501188130085159785113344, 648740172906485727983524271405824, 22591360806791558877526051411343415296, 1567817808096346724727108606144936617617408, 216926754380646324945248257231539109504762560512, 59860937747979290094875740320161640032623120090828800]
#A323875 for i=2
NuKcomp(20, 3);
 [0, 0, 1, 6, 55, 825, 20818, 925036, 76321756, 12143833740, 3786364993664, 2323363153263768, 2810644049356050752, 6714880790313869814368, 31734660624638397560681792, 297106568651256947892439231872, 5516820501457062391874183605225216, 203371936690880564729559424288326233856, 14896201998273652941883043518617399703696384, 2169416538066466491819023076937523996727138210304]
#A323876 for i=3
NuKcomp(20, 4);
 [0, 0, 0, 1, 10, 125, 2275, 64673, 3102204, 272277040, 46202044900, 15442093276764, 10171924771814520, 13188852179018387144, 33674263441006260931040, 169522275849148918884400912, 1685048703908907788901122512512, 33116110237646373502366665503208064, 1288337109916947580133035603563656989952, 99320901948403913391024993536094346775110656]
#A323877 for i=4
NuKcomp(20, 5);
 [0, 0, 0, 0, 1, 15, 245, 5320, 169113, 8692845, 803632060, 144006917010, 51190235706324, 35973349034458836, 49733014749298407800, 135098732052853350832960, 721623817888224485383613072, 7589231274657209868572623947024, 157373724998165331860030332231216576, 6443260493678153802385273326576384600800]
#Not in the OEIS
#Thus, the smallest i for which it is not in the OEIS is i=5.