#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
#p6FirstLast.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

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

# Question 1: Let K be the 3-digit number consisting of your 3rd, 4th, and 5th RUID digits?
# What is g(K)? 

# Answer 1: My RUID is 193002246. K = 300. g(K) = 160808762893084890404249090419201806693140218500453352447509801.


# Question 2: Is {g(n)} in the OEIS? If yes, what is the A-Number? If not, should it be? 

# Answer 2: {g(n)} is not in the OEIS. I don't think it should necessarily be in the OEIS
# since I don't feel like it has that much significance.

# Question 3: For 1 = 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?

# Answer 3: 
# SeqRec([[1 $ 3], [0 $ (3 - 1), 1]], 30);
#[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] --> A000073


# SeqRec([[1 $ 4], [0 $ (4 - 1), 1]], 30);
# [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] --> A000078


# SeqRec([[1 $ 5], [0 $ (5 - 1), 1]], 30);
# [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] --> A001591


# SeqRec([[1 $ 6], [0 $ (6 - 1), 1]], 30);
# [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] --> A001592


# SeqRec([[1 $ 7], [0 $ (7 - 1), 1]], 30);
# [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] --> A122189


# SeqRec([[1 $ 8], [0 $ (8 - 1), 1]], 30);
# [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] --> A079262


# SeqRec([[1 $ 9], [0 $ (9 - 1), 1]], 30);
#  [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 
#    511, 1021, 2040, 4076, 8144, 16272, 32512, 64960, 129792, 
#    259328, 518145, 1035269, 2068498] --> A104144


# SeqRec([[1 $ 10], [0 $ (10 - 1), 1]], 30);
# [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 
#   512, 1023, 2045, 4088, 8172, 16336, 32656, 65280, 130496, 
#   260864, 521472, 1042432] --> A122265


# SeqRec([[1 $ 11], [0 $ (11 - 1), 1]], 30);
# [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 
#   256, 512, 1024, 2047, 4093, 8184, 16364, 32720, 65424, 130816, 
#   261568, 523008] --> A168082


# SeqRec([[1 $ 12], [0 $ (12 - 1), 1]], 30);
# [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 
#   256, 512, 1024, 2048, 4095, 8189, 16376, 32748, 65488, 130960, 
#   261888] --> A168083


# SeqRec([[1 $ 13], [0 $ (13 - 1), 1]], 30);
# [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 
#   128, 256, 512, 1024, 2048, 4096, 8191, 16381, 32760, 65516, 
#   131024] --> A168084


# SeqRec([[1 $ 14], [0 $ (14 - 1), 1]], 30);
# [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 
#   64, 128, 256, 512, 1024, 2048, 4096, 8192, 16383, 32765, 65528]


# SeqRec([[1 $ 15], [0 $ (15 - 1), 1]], 30);
# [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 
#   64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32767]

# The smallest i that is not present in the OEIS is i=14. I don't particularly think it
# needs to show up in OEIS. 

# Question 4: Let #a:=2nd digit of your RUID (if it is 0 make it 1), b:=7th digit, then what is the
# 100th term of GFSEQ(1/(1-x^a-x^b)). 

# Answer 4: My RUID is 193002246. a=9 and b=2.The 100th term is 857602.