#ATTENDANCE QUIZ FOR LECTURE 16 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p16
#with an attachment called
#p16FirstLast.txt
#(e.g. p16DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Oct. 30, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

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

Attendance question 1 
Convert the following recurrence to explicit form 

6*f(n)+12*fn(n+1)+18*f(n+3) = 0

Answer 1:
f(n+3) = 1/3f(n) - 2/3(f(n+1))

Attendance question 2

Find F(6) and F(5)

f(n) = 3*f(n-1)-4*f(n-1), f(0)=1, f(1) = -2
f(5) = 10
f(6) = 134

Attendance question 3
What is F(10^6)? How long did it take? What is f(10^6) how long did it take?

F(10^6)
Took too much time
f(10^6)
Too many levels of recurssion

Attendance question 4
Consider the sequence that is defined by the recurrence 
f(n+1000) = f(n+999) + 5*f(n)


Attendance question 5
Characterize the sequence that satisy a (Homog) reccurenece of order zero
Total degree of each term is the same
The degree is zero of each term

Attendance problem 6
Can you prove that d(n)/n! = 1/e

Answer - der = n! * sum((-1)^k/k!, k=0..n)
e^x = sum(x^i/i!, i =0..infinity)
Ths we have lin x-> infiity der(n)/n! = 1/e

Attendance problem 7
What is the OEIS number of this sequence
1, 1, 2, 4, 10, 26, 76, 232, 2620, ...

A000085		Number of self-inverse permutations on n letters, also known as involutions; number of standard Young tableaux with n cells.

Attendance problem 8
Find the operators in N and N6(-1) annihilated by w(n)
w(n) = w(n)+w(n-1)+(n-1)*w(n-2)

Attendance problem 9
Look up the syntax of
 Do SumTools[Hypergeometric]ZeilbergerReccurence
 
 ZeilbergerRecurrence(T, n, k, f, l..u)

T
-
hypergeometric term of n and k
n
-
name
k
-
name
En
-
name; denote the shift operator with respect to n
f
-
name of the recurrence function
l..u
-
range for k
'Zpair'
-
list of two elements specifying a Z-pair for T