Kenneth Chan
#ATTENDANCE QUIZ FOR LECTURE 17 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p17
#with an attachment called
#p17FirstLast.txt
#(e.g. p17DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Nov. 3, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH, BY THE ANSWER
Question 1
(i)Is this in the OEIS(including the 3 at the beginning) What is the A number
(ii)Without the beginning 3 it is, what is the a number
(iii) is the King Tours mentioned in the OEIS in our meaning?
Answer
(i)A198633
(ii)A020707
(iii)Yes

Question 2
(i)How many members of Cn(n) are there with an Even Number of 1's?
(ii) How many are there with a number of 1's that is divisible by 4 
Answer
(i)2^n
(ii)2^n-1

Question 3
(i)List of the Neighbors of [1,1,1,1,1] in Bn(5)
(ii)How many neighbors does [1,1,1,1....,1] (1 repeared 10^100 times in 
Bn(10^1000) have?
Answer
(i)5
(ii)10^1000

Question 4
Is this sequence in the OEIS?
Answer
Yes A318109

Question 5
What is the A-number of this sequence?
Is that the main reason why it is there?
Is the fact that it is the diagonal sequence of 1/(1-x-y-z+4*x*y*z) mentioned there?
Answer
A000172
It gives Cusick a general method of deriving recurrences for the r-th order Franel numbers
yes it is(Diagonal of rational function 1 / ((1-x)*(1-y)*(1-z) - x*y*z). - Seiichi Manyama, Jul 11 2020)