#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:

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

1) 
185002317
Let a[i] be the i-th digit of your RUID (if it is zero make it 1)
In how many ways can you walk from 0 to 131 using as fundamental steps
the set {a[3],a[5],a[9]}
{5,1,7}

4517823721565575062

2)
Is this sequence in the OEIS?
f:=normal(1/(1-(x+x^4)/(1-x^5)));
seq(coeff(taylor(f,x=0,41),x,i),i=0..40);

No, it is not on the OEIS

3)
Let f(x)=1/(1-4*x-x^6);
(i) Find the coefficient of x^100 in the taylor expansion of f(x)
1644594257296515568488059327938971072084521685469936722570496
(ii) Find the coefficient of x^101 in the taylor expansion of f(x)
6579981121576468112367189280234473995254094130576501178758144
How far is a(100)/a(101) from the real root of 1-4*x-x^6
0.00006094593

4)
In how many ways can a chess king walk from one corner of
the chess board to the opposite corner? 

using 1/(1-x-y-x*y)

DiagWalks2D({[0, 1], [1, 0], [1, 1]}, 7)[8] => 48639

5)
Is this sequence in the OEIS?
seq(A(i,i),i=0..20);
1,2,14,106,838,6802,56190,470010,3968310,33747490,288654574,2480593546,21400729382,
185239360178,1607913963614...

Yes, it is A051708