#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:3

#1.How many connected graphs are there with 30 vertices and 50 edges?
#we use the given functions,
L := WtEdConGclever(30, a)[30];
coeff(L, a, 50);
616531513027177775473601317524937092680978914590598004251998471840

########################################################################################

#2.How many LABELLED connected graphs are there with 30 vertices and 50 edges?


#answer:This is basically ATreeSeq(30, 21) as 50 edges are (30-1+21)
ATreeSeq(30, 21)[30];
616531513027177775473601317524937092680978914590598004251998471840 

#########################################################################################

#3. For i=1,2,3,4...
#Find the OEIS A-number 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

NuKcomp(20, 3);
  [0, 0, 1, 6, 55, 825, 20818, 925036, 76321756, 12143833740, 

    3786364993664, 2323363153263768, 2810644049356050752, 

    6714880790313869814368, 31734660624638397560681792, 

    297106568651256947892439231872, 

    5516820501457062391874183605225216, 

    203371936690880564729559424288326233856, 

    14896201998273652941883043518617399703696384, 

    2169416538066466491819023076937523996727138210304]
#A323876

NuKcomp(20, 4);
[0, 0, 0, 1, 10, 125, 2275, 64673, 3102204, 272277040, 

  46202044900, 15442093276764, 10171924771814520, 

  13188852179018387144, 33674263441006260931040, 

  169522275849148918884400912, 1685048703908907788901122512512, 

  33116110237646373502366665503208064, 

  1288337109916947580133035603563656989952, 

  99320901948403913391024993536094346775110656]
#A323877
#and so on...

NuKcomp(20, 5);
[0, 0, 0, 0, 1, 15, 245, 5320, 169113, 8692845, 803632060, 

  144006917010, 51190235706324, 35973349034458836, 

  49733014749298407800, 135098732052853350832960, 

  721623817888224485383613072, 7589231274657209868572623947024, 

  157373724998165331860030332231216576, 

  6443260493678153802385273326576384600800]
#This is not in OEIS
#So i=5 is the smallest i