> read `M21.txt`; Help21();Help18();
` WtEdConG(N,a), WtEdConGclever(N,a), ProbConn(n,m), EstProbConn(n,m,N),
NuKcomp, AvCCseq(n) , ,FindCutOff(n,co)`
` LT(n) , LTseq(N) LTseqC(N) ` ` CF(E,n) , AllGraphs(n) RandGr(n,K) , CC(G,i),
CCs(G) , AllConGraphs(n), AllConGraphs(n) ` `AllGraphsK(n,K) ,
AllConGraphsK(n,K), NuConG(N), NuConGclever(N)`
> #Attendence Q1.
> #How many connected graphs are there with 30 vertices and 50 edges?
> coeff(WtEdConGclever(30,a)[30],a,50);
616531513027177775473601317524937092680978914590598004251998471840
> 
> #Attendence Q2:
> #How many labeled conected graphs are there with 30 vertices and 50 edges?
> coeff(WtEdConGclever(30,a)[30],a,50);
616531513027177775473601317524937092680978914590598004251998471840
> 
> 
> #Attendence Q3:
> #for i=2,3,4,5
> #find the OEIS A-number of
> #NuKcomp(20,i)
> #What is the smallest i for which it is not in the OEIS?
> #For i = 2,
> NuKcomp(20,2);
[0, 1, 3, 19, 230, 5098, 207536, 15891372, 2343580752, 675458276144,
383306076989440, 430041136692146912, 956431386434331323776,
4224539434553753578497024, 37106501188130085159785113344,
648740172906485727983524271405824, 22591360806791558877526051411343415296,
1567817808096346724727108606144936617617408,
216926754380646324945248257231539109504762560512,
59860937747979290094875740320161640032623120090828800]
> #A323875: Number of labeled graphs on n nodes with two connected components.
> 
> #For i = 3,
> NuKcomp(20,3);
[0, 0, 1, 6, 55, 825, 20818, 925036, 76321756, 12143833740, 3786364993664,
2323363153263768, 2810644049356050752, 6714880790313869814368,
31734660624638397560681792, 297106568651256947892439231872,
5516820501457062391874183605225216, 203371936690880564729559424288326233856,
14896201998273652941883043518617399703696384,
2169416538066466491819023076937523996727138210304]
> #A323876: Number of labeled graphs on n nodes with three connected components.
> 
> #for i = 4,
> NuKcomp(20,4);
[0, 0, 0, 1, 10, 125, 2275, 64673, 3102204, 272277040, 46202044900,
15442093276764, 10171924771814520, 13188852179018387144,
33674263441006260931040, 169522275849148918884400912,
1685048703908907788901122512512, 33116110237646373502366665503208064,
1288337109916947580133035603563656989952,
99320901948403913391024993536094346775110656]
> #A323877: Number of labeled graphs on n nodes with four connected components.
> 
> #for i = 5,
> 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.
> #5 is the smallest not in the OEIS.