#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

#Attendance Problem #1.
#Let K be the 3-digit number consisting of your 3rd,4th,5th RUID digits
#what is g(K)?
#Answer: Given my RUID as 197005262, K={700,070,007}
#then G(700) = {}, G(070) = {}, G(007) = {[3,4],[4,3]}
#so g(K)= 2

#attendance Probelm #2.
#Is {g(n)} in the OEIS? If yes, what is the A-number / If not, should it be?
#answer: for {g(n)} = {1,1,0,1,3,2,0,2,0,0...}, there is no A-number for it and since later seq only provide 0's it is irrelevant.

#attendance Probelm #3.
#For i=3,4,5, ...
#Compute SeqRec([[1$i],[0$(i-1),1]],30):
#for i =3,
SeqRec([[1 $ 3], [0 $ 2, 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] #Tribonacci numbers

#for i =4,
SeqRec([[1 $ 4], [0 $ 3, 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] #Tetranacci

#The OEIS show only up to 13-step fibonnaci. So the answer is when i = 14



#attendance Probelm #4.
#Let a:=2nd digit of your RUID (if it's 0, make it 1), b:=7th digit
#what is the 100th term of 
#GFseq(1/(1-x^a-x^b)
#answer: given RUID as 197005262,  a:=9; b:=2
#then, GFseq(1/(1-x^9-x^2),x,100) gives us 739882 as 100th term.