#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 ith digit of your RUID (if it is 0, make it 1)
In how many ways can you walk from 0 to 131 using as fundamental steps {a[3],a[5],a[9]}?

My RUID: 193006310
Fundamental steps: {3,1,1} --> same as {3,1}



3414277392316082958344 different walks

2. Is this sequence in the OEIS?

Sequence: 1, 1, 1, 1, 2, 3, 5, 7, 10, 15, 23, 35, 52, 77, 115, 173, 260, 389, 581, 869, 1302, 1951, 2921, 4371, 6542, 9795, 14667, 21959, 32872, 49209, 73671, 110297, 165128, 247209, 370089, 554057, 829482, 1241819, 1859117, 2783263, 4166802

No, this sequence is not in the OEIS.



3. Let f(x) be 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(101)/a(100) from the real root of 1-4x-x^6?

5.50212600691796907411698226384624972901408964414007610557115605536719084166213389544106303*10^(-10)



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

48639



5. Is this sequence in the OEIS?

Sequence: 1, 2, 14, 106, 838, 6802, 56190, 470010, 3968310, 33747490, 288654574, 2480593546, 21400729382, 185239360178, 1607913963614, 13991107041306, 122002082809110, 1065855419418690, 9327252391907790, 81744134786314410, 717367363052796678

Yes, this sequence is in the OEIS. The OEIS number is A051708.