#ATTENDANCE QUIZ FOR LECTURE 9 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p9
#with an attachment called
#p9FirstLast.txt
#(e.g. p9DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Oct. 6, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 5

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



#ATTENDANCE Q. #1 for LECTURE 9
#Let a[i] be the ith digit of your RUID (if 0 make it 1), how many walks from 0 to 131 using a[3],a[5],a[9]? (192002142) --> 2,1,2 --> {1,2}

#ANSWER to Q. #1:	1725375039079340637797070384 walks




#ATTENDANCE Q. #2 for LECTURE 9
#Is that sequence in the OEIS? 

#ANSWER to Q. #2:	Yes, and I found one with number A116975 after omitting the first couple of terms




#ATTENDANCE Q. #3 for LECTURE 9
#(i) Find the coefficient of x^100 in the Taylor expansion of f(x)=1/(1-4*x-x^6)
#(ii) Find the coefficient of x^101 in the Taylor expansion of f(x)=1/(1-4*x-x^6)
#How far is a(100)/a(100) from the real root of 1-4*x-x^6?

#ANSWER to Q. #3:

#	(i) 1644594257296515568488059327938971072084521685469936722570496
#	(ii) 6579981121576468112367189280234473995254094130576501178758144
#	The ratio is approx. 2*10^(-71) away from the positive real root of denom(f)




#ATTENDANCE Q. #4 for LECTURE 9
#How many ways can a chess king walk from one corner of the chess board to the opposite corner?

#ANSWER to Q. #4:	DiagWalks2D({[1,0],[0,1],[1,1]},7)[8]  =  48639 ways




#ATTENDANCE Q. #5 for LECTURE 9
#Is that [rook] sequence in the OEIS?

#ANSWER to Q. #5:	Yes, this is in the OEIS. A051708: "Number of ways to move a chess rook from the lower left corner 
#			to square (n,n), with the rook moving only up or right."