#ATTENDANCE QUIZ FOR LECTURE 14 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p24
#with an attachment called
#p24FirstLast.txt
#(e.g. p24DoronZeilberger.txt)

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


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

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


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 3

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




#ATTENDANCE Q. #1 for LECTURE 24
#write all integer partitions of 7

#ANSWER to Q. #1:	

# 7, 6+1, 5+2, 5+1+1, 4+3, 4+2+1, 4+1+1+1, 3+3+1, 3+2+2, 3+2+1+1, 3+1+1+1+1, 2+2+2+1, 2+2+1+1+1, 2+1+1+1+1+1, 1+1+1+1+1+1+1




#ATTENDANCE Q. #2 for LECTURE 24
# write the number of partitions of 7 into distinct parts and the number of integer partitions of 7 into odd parts

#ANSWER to Q. #2:
# 7, 5+1+1, 3+3+1, 3+1+1+1+1, 1+1+1+1+1+1+1 = 5
# 7, 6+1, 5+2, 4+3, 4+2+1 = 5

#Yes, they are the same number (5=5)





#ATTENDANCE Q. #3 for LECTURE 24
#A number of 1,2,3,5,7,11,15,22,30 ... in OEIS

#ANSWER to Q. #3:

#A000041





#ATTENDANCE Q. #4 for LECTURE 24
#who wrote the classic book on the theory of partitions, what is his birth date?


#ANSWER to Q. #4:

#George Andrews wrote it (1976), his birth date is December 4, 1938 





#ATTENDANCE Q. #5 for LECTURE 24
#A number of 1,1,2,2,3,4,5,6,8,...?


#ANSWER to Q. #5:

#A000009




#ATTENDANCE Q. #6 for LECTURE 24
#A number of 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 14, 17, 19, 23, 26, 31?


#ANSWER to Q. #6:

#A003114




#ATTENDANCE Q. #7 for LECTURE 24
#Whose theorem is it that these above two sequences are the same?

#ANSWER to Q. #7:

#Leonard James Rogers & Srinivasa Ramanujan





#ATTENDANCE Q. #8 for LECTURE 24
#Whose theorem is it that these above two sequences are the same?

#ANSWER to Q. #8:

#Leonard James Rogers & Srinivasa Ramanujan




#ATTENDANCE Q. #9 for LECTURE 24
#A number of 6,27,98,315,913,2462..?


#ANSWER to Q. #9:

#A071734




#ATTENDANCE Q. #10 for LECTURE 24
#i) Does there exist a k between 0 and 6 s.t. seq(pn(7*n+k)/7,n=1..60) is an integer sequence? (A number)?
#ii) Same but for 11 instead of 7?


#ANSWER to Q. #10:

# i) Yes, k=5,  A071746
# ii) Yes, k=6, A076394
# I didn't find any others from random experimenting, but on the OEIS there is one for p(49*n + 47)/49, and likely others, too



#ATTENDANCE Q. #11 for LECTURE 24
#Why should Dr. Z from now on make you watch the lectures before the recitation?


#ANSWER to Q. #11:

#since recitation is meant to repeat/review material taught during the lectures of a particular week