#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

Question 1: In how many ways using as fundamental steps a[3] = 4, a[5] = 1, a[9] = 9 can you reach 131

Answer 1: These many ways 26946771861312745193

Question 2: Is the sequence that Dr. Z created in the OEIS?

Answer 2: No it is not

Question 3: Let f(x) = 1/(1-4*x-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(101)?

Answer 3:
coeff(taylor(f, x = 0, 101), x, 100);
 1644594257296515568488059327938971072084521685469936722570496
coeff(taylor(f, x = 0, 102), x, 101);
 6579981121576468112367189280234473995254094130576501178758144

 Maple upto 50 digits is showing no variation in numbers

 Question 4:
 In how many ways can a chess king walk from one corner to the other?
 Answer 4:
 I cannot figure out what f(x) would be. 

 Question 5:
 Is the rook sequence in OEIS?

 Answer 5: Yes it is. A51708