#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
#p8FirstLast.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

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Attendance Problem 1:

Let a[i] be the ith digit of my RUID (if 0, make it 1)

How many ways can you walk from 0 to 131 using as fundamental steps the set {a[3],a[5],a[9]} = {6, 1, 9}?

GFseq(CompsGF({1,6,9},x),x,131)[132] = 11043240405876650 ways to walk from 0 to 131 using the above fundamental steps.


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Attendance Problem 2:

Is the sequence in the OEIS? 

Yes, the sequence in the OEIS is A116975.

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Attendance Problem 3:

Let f(x) = 1 /(1-4x-x^6);
(i) Find the coefficient of x^100 in the Taylor expansion of f(x)
(ii)Find the coefficient of x^101 in the Taylor expansion of f(x)
How far is a(100) / a(100) from the real root of 1-4x-x^6?
(I think you meant a(100) / a(101))
 
i.) GFseq(f,x,101)[101] = 
1644594257296515568488059327938971072084521685469936722570496

ii.) GFseq(f,x,101)[102] = 6579981121576468112367189280234473995254094130576501178758144

a(100) / a(101) is 0.2481341913481519967735772810e-72 away from the real root of the expression.


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Attendance Problem 4:

In how many ways can a chess king walk from one corner of the chess board to the opposite corner? (assuming forward moving)

DiagWalks2D({[1,0],[0,1],[1,1]},8)[9] = 265729 ways.

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Attendance Problem 5:

Is the sequence in the OEIS?

Yes, the sequence in the OEIS is A051708.