#ATTENDANCE QUIZ FOR LECTURE 7 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p7
#with an attachment called
#p7FirstLast.txt
#(e.g. p7DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Sept. 28, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

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

#Attedance problem #1 for lecture 7

#Q:Let K be the 3-digit number consisting of your 3rd, 4th, 5th RUID digits. What is g(K)?

#A: Since K is 600 (out of 186000032), we find that g(600) = (-2/5 - (2*sqrt(5))/5)*(1/2 - sqrt(5)/2)^600 + ((2*sqrt(5))/5 - 2/5)*(1/2 + sqrt(5)/2)^600 + 4/5 using rsolve (i.e. eval(rsolve({x(0) = 0, x(1) = 1, x(2) = 0, x(3) = 3, x(4) = 4, x(n) = x(n - 1) + x(n - 3) + x(n - 4)}, x(n)), n = 600)). This leads to g(600) roughly equal to 1.2209180004×10^(125)

# We also find that k is too large for maple to output an answer

#Attedance problem #2 for lecture 7

#Q:Is {g(n)} in the OEIS? If Yes what is the A-number, if not should it be?

#A:{g(n)} cannot be found in OEIS (from what I found), however it should be in OEIS


#Attedance problem #3 for lecture 7

#Q:For i=3, 4, 5, ...; Compute SeqRec([[1$i],[0$(i-1)],1],30). Find whether these sequences are in the OEIS and find their A-numbers. What is the smallest i for which this sequence is not in the OEIS? Should it be?

#A:SeqRec([[1$i],[0$(i-1)],1],30) this sequence fails at every instance from even 3. Thus 3 is the smallest i for which the sequence is not found in OEIS and shouldn't be in OEIS as it isn't useful at all.


#Attedance problem #4 for lecture 7

#Q:Let a:=2nd digit of your RUID (it is 0 make 1) b:=7th digit. What is the 100th term of GFseq(1/(1-x^a-x^b))

#A:498657124 (given that a is 8 and b is 1)