#ATTENDANCE QUIZ FOR LECTURE 7 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p7
#with an attachment called
#p7FirstLast.txt
#(e.g. p7DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Sept. 28, 2020, 8:00pm


#THE NUMBER OF ATTENDANCE QUESTIONS WERE: 4 questions

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

#1) Let K be the 3-digit number consisting of your 3rd, 4th, 5th RUID digits
#My RUID is 185002317: K=500
#What is g(K)? 
#g(500)=163239554609501374551452493595724700017620846265794375806005112440749890967784788181321124006922685358001

#2) Is {g(n)} in the OEIS? If Yes what is the A number? If not should it be?
#g(n) is 1, 1, 1, 2, 4, 6, 9, 15, 25, 40, 64, ...
#Yes it is, A006498

#3) For i=3, 4, 5, ...
#compute
#SeqRec([[1$i],[0$(i-1),1]],30);
#Find whether these sequences are in the OEIS
#Find their A-numbers
#What is the smallest i for which this sequence is not in the OEIS?
#Should it be?

#i=3: 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012, 121415, 223317, 410744, 755476, 1389537, 2555757, 4700770, 8646064, 15902591
#Yes it is in the OEIS as A000073

#i=4: 0, 0, 0, 1, 1, 2, 4, 8, 15, 29, 56, 108, 208, 401, 773, 1490, 2872, 5536, 10671, 20569, 39648, 76424, 147312, 283953, 547337, 1055026, 2033628, 3919944, 7555935, 14564533, 28074040
#Yes it is in the OEIS as A000078

#i=5: 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 61, 120, 236, 464, 912, 1793, 3525, 6930, 13624, 26784, 52656, 103519, 203513, 400096, 786568, 1546352, 3040048, 5976577, 11749641, 23099186
#Yes it is in the OEIS as A001591

#i=6: 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 63, 125, 248, 492, 976, 1936, 3840, 7617, 15109, 29970, 59448, 117920, 233904, 463968, 920319, 1825529, 3621088, 7182728, 14247536
#Yes it is in the OEIS as A001592

#i=7: 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 127, 253, 504, 1004, 2000, 3984, 7936, 15808, 31489, 62725, 124946, 248888, 495776, 987568, 1967200, 3918592, 7805695
#Yes it is in the OEIS as A122189

#i=8: 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 255, 509, 1016, 2028, 4048, 8080, 16128, 32192, 64256, 128257, 256005, 510994, 1019960, 2035872, 4063664,
#Yes it is in the OEIS as A079262

#i=9:
#Yes, A104144	

#i=10:
#A122265

#i=11:
#A168082

#i=12:
#A168083

#i=13:
#A168084	

#i=14: 
#No, not in the OEIS

#The smallest i value that is not in the OEIS is i=14.

#It should be added because the OEIS is a database of sequences, so I think that it should be included even if it is not some vital 
#sequence representing something, somewhere. Plus, they have cool names. I would guess, though, that the fibonacci i-step sequences are 
#probably only useful up until a certain point, so it is not super important to have it added.

#4) RUID:185002317
#Let a:=2nd digit of your RUID (if it is 0 make it 1) = 8
#b:=7th digit = 3
#What is the 100th term of 
#GFseq(1/(1-x^a-x^b))

#The 100th term is 152857.