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


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 4


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


1. Q: Let a[i] be the i-th digit of your RUID. In how many ways can you walk from 0 to 131 using the fundamental steps the set {a[3], a[5], a[9]}?


A: 132


2. Q: Is this sequence in the OEIS?


A: No


3. Q: Let f(x) = 1/(1-4x-x^6)


1. Find the coefficient of x^100 in the Taylor expansion of f(x)
2. 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


A: 


I. 1644594257296515568488059327938971072084521685469936722570496
II. 6579981121576468112367189280234473995254094130576501178758144


4. Q: in how many ways can a chess king walk from one corner of the chess board to the opposite corner? 


A: 65