#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

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, 5th RUID number. What is g(k)?

ANSWER:

For k = 101, we have that g(101) = 414733676044142633476.

QUESTION #2:

Is {g(n)} in the OEIS? If YES what is the A-number, if not should it be?

ANSWER:

{g(10)} = 1, 1, 0, 1, 3, 4, 5, 9, 16, 25, 39.
Searching this in OEIS resulted in no hits. I believe it should be there as g(n) = g(n-1) + g(n-3) + g(n-4) seems like it may be common. 


QUESTION #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 the sequence is not in the OEIS? Should it be?

For 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
A-number: A000073

For 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
A-number: A000078

For 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
A-number: A001591

The smallest i I found which had no sequence in the OEIS was i = 14. It looks very similar to the sequence of 2^n which delayed by a number. Therefore, I think it should be in the OEIS.


QUESTION #4:

Let a:=2nd digit of RUID, b:=7th digit of RUID. What is the 100th term of GFSeq(1/1-x^a-x^b)

ANSWER:

a = 7, b = 6. 100th term of GFseq(1/1-x^7-x^6,x,100) is 0.