#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

1. Let K be a 3-digit number consisting of your 3rd, 4th and 5th RUID digits. 
What is g(K)?
A1. 
K:= {3,0,0}
G(0)= {[]}, G(1)= {}, G(2)= {}, G(3)= {[3,0],[0,3]}, G(4) = {}
g(k) = |G(k)|
g(k) = 0*g(k-1) + 0*g(k-2) + 2*g(k-3) + 0*g(k-4)
initial conditions: g(0)=1, g(1)=0, g(2)=0, g(3)=2
[0,0,2,0],[1,0,0,2]
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2. Is g(n) in the OEIS? If yes what is the A-number? If not should it?
A2.
The list of g(n) = {1,1,0,1,3,4,5,9,16,25,39,..}
This list is not there on OEIS and it shouldn't be added because these are list that vary according 
to the g(n) recurrence that is derived. Hence they are not going to be similar 
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3. For i=3,4,5,...
Compute
SeqRec([[1$i],[0$(i-1),1]],30);
Find whether their sequences are on OEIS and find their A numbers
What is the smallest i for which there is no OEIS sequence
A3.
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]
A number: 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]
A number: 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]
A number: A001591

Smallest value of i with no sequence in OEIS:
i = 0
This operation FAILS on compile in MAPLE as the value returns negative and hence has no OEIS sequence 
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4. Let a:=2nd digit of RUID, b:= 7th digit RUID
What is the 100th term of GFseq(1/1-x^a - x^b)
A4.
GFseq(1/(-x^8 - x^3 + 1), x, 100);
[1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 3, 1, 1, 4, 1, 3, 5, 

  1, 6, 6, 2, 10, 7, 5, 15, 8, 11, 21, 10, 21, 28, 15, 36, 36, 

  26, 57, 46, 47, 85, 61, 83, 121, 87, 140, 167, 134, 225, 228, 

  217, 346, 315, 357, 513, 449, 582, 741, 666, 928, 1056, 1023, 

  1441, 1505, 1605, 2182, 2171, 2533, 3238, 3194, 3974, 4743, 

  4799, 6156, 6914, 7332, 9394, 10108, 11306, 14137, 14907, 

  17462, 21051, 22239, 26856, 31159, 33545, 40993, 46066, 51007, 

  62044, 68305, 77863, 93203, 101850, 118856, 139269, 152857, 

  180900]
100th term of sequence: 180900
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