#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

1. Let a[i] be the i-th digit of your RUID (if zero make it 1)
In how many ways can you walk from 0 to 131 using as fundemental steps the 
set {a[3],a[5],a[9]}
A1. 

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2. Is seq(coeff(taylor(f,x=0,41),x,i),i=0..40); on OEIS?
A2. It is not on OEIS
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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 the a(100)/a(101) from the real root of 1-4*x-x^6
A3.
a := n -> coeff(taylor(1/(-x^6 - 4*x + 1), x = 0, n + 1), x, n);
a := proc (n) options operator, arrow; coeff(taylor(1/(-x^6-4*x+\

  1), x = 0, n+1), x, n) end proc


a(100);
 1644594257296515568488059327938971072084521685469936722570496

a(101);
 6579981121576468112367189280234473995254094130576501178758144

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4. In how many ways can a chess King walk from one corner of the 
chess board to the opposite corner?
A4. f := normal(1/(1 - x/(1 - x) - y/(1 - y)));
                          (-1 + x) (-1 + y)  
                   f := ---------------------
                        3 x y - 2 x - 2 y + 1

A := (m, n) -> coeff(taylor(coeff(taylor(f, x = 0, m + 1), x, m), y = 0, n + 1), y, n);
A := proc (m, n) options operator, arrow; coeff(taylor(coeff(tay\

  lor(f, x = 0, m+1), x, m), y = 0, n+1), y, n) end proc


A(7, 7);
                             470010
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5. Is this sequence on OEIS: 
seq(A(i, i), i = 0 .. 20);
  1, 2, 14, 106, 838, 6802, 56190, 470010, 3968310, 33747490, 

    288654574, 2480593546, 21400729382, 185239360178, 

    1607913963614, 13991107041306, 122002082809110, 

    1065855419418690, 9327252391907790, 81744134786314410, 

    717367363052796678

A5. A number: A051708
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