#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: 5

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH, BY THE ANSWER
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1. (i) Is this in the OEIS (including the 3). If so, what is the A-number?
	3,4,8,16,32,64,128,256,512
	A-number :=  A198633
   (ii) Without 3in the beginning, is it? What is the A-number?
	4,8,16,32,64,128,256,512
	A-number := A000079
   (iii) Is the King's Tour mentioned in the OEIS in our meaning?
	Kings Tour is not mentioned on OEIS

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2. (i) How many members of Cn(n) are with even number of 1's?
	Members with even number of 1's in Cn(n) := n
   (ii) How many are there with a number of 1's divisible by 4
	If n > 4, then number of 1's divisible of 4 := 0,4,8,...
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3. (i) List the neighbors of [1,1,1,1,1] in Bn(5)
	Bn(5)[1];
[{2, 3, 5, 9, 17}, {1, 4, 6, 10, 18}, {1, 4, 7, 11, 19}, 

  {2, 3, 8, 12, 20}, {1, 6, 7, 13, 21}, {2, 5, 8, 14, 22}, 

  {3, 5, 8, 15, 23}, {4, 6, 7, 16, 24}, {1, 10, 11, 13, 25}, 

  {2, 9, 12, 14, 26}, {3, 9, 12, 15, 27}, {4, 10, 11, 16, 28}, 

  {5, 9, 14, 15, 29}, {6, 10, 13, 16, 30}, {7, 11, 13, 16, 31}, 

  {8, 12, 14, 15, 32}, {1, 18, 19, 21, 25}, {2, 17, 20, 22, 26}, 

  {3, 17, 20, 23, 27}, {4, 18, 19, 24, 28}, {5, 17, 22, 23, 29}, 

  {6, 18, 21, 24, 30}, {7, 19, 21, 24, 31}, {8, 20, 22, 23, 32}, 

  {9, 17, 26, 27, 29}, {10, 18, 25, 28, 30}, 

  {11, 19, 25, 28, 31}, {12, 20, 26, 27, 32}, 

  {13, 21, 25, 30, 31}, {14, 22, 26, 29, 32}, 

  {15, 23, 27, 29, 32}, {16, 24, 28, 30, 31}]

   (ii) How many neighbors does [1,1,1,...,1] (1 repeated 10^100 times) in Bn(10^100) have?
	From seeing that nops(Bn(5)[1]) := 32 := 2^5
                         nops(Bn(10)[1]):= 1024 := 2^10
	Hence nops(Bn(10^100)[1]) := 2^(10^100)

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4. Is this sequence on OEIS? DiagSeq3(1/1-x-y-z+2*x*y*z),x,y,z,50)
	Yes. A-number := A318109
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5. (i) What is the A-number of this sequence? DiagSeq3(1/1-x-y-z+4*x*y*z),x,y,z,50)
	A-number := A000172
   (ii)Is that the main reason it is there? Is the fact that it is diagonal equence of 
	1/(1-x-y-z+4*x*y*z) mentioned there?
	It is described as the taylor expansion of a special point on a curve described by 
	Beauville. It's aso mentioned that is it the diagonal of rational 
	function 1/(1 - x - y - z + 4*x*y*z)

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