> #Attendence Q1.
> #Write down the set all the integers partition of 7.
> #1+3+4+3+2+1+1 = 15
> #With 1 part: {[7]}
> #With 2 part: {[1,6], [2,5], [3,4]}
> #With 3 part: {[1,1,5], [1,2,4],[1,3,3],[2,2,3]}
> #With 4 part: {[1,1,1,4], [1,1,2,3], [1,2,2,2]}
> #With 5 part: {[1,1,1,1,3], [1,1,1,2,2]}
> #With 6 part: {[1,1,1,1,1,2]}
> #With 7 part: {[1,1,1,1,1,1,1]}
> 
> #Attendence Q2.
> #Write down the set of partitions of 7 into distinct parts, and write the explicit the number of integer partitions of 7 into odd parts including 7. Find out whether it's same number. 
> #With 1 part: {[7]}
> #With 2 part: {[1,6], [2,5], [3,4]}
> #With 3 part: {[1,2,4]}
> #With 4 part: {}
> #With 5 part: {}
> #With 6 part: {}
> #With 7 part: {}
> 
> #With 1 part: {[7]}
> #With 2 part: {}
> #With 3 part: {[1,1,5],[1,3,3]}
> #With 4 part: {}
> #With 5 part: {[1,1,1,1,3]}
> #With 6 part: {}
> #With 7 part: {[1,1,1,1,1,1,1]}
> #Both have 5 partitions. Same.
> 
> #Attendence Q3.
> read `M24.txt`;
`For a list of the SET procedures, type: Help24s();`
`For a list of the ENUMERATION procedures (via Dynamic programming), type: Help24e();`
`For a list of the GENERATING functions procedures  type: Help24g();`
> seq(nops(Pn(i)), i=1..20);
1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627
> #What is the A-number of this sequence?
> #A000041: a(n) is the number of partitions of n
> 
> #Attendence Q4.
> #Who wrote the classic book on the theory of partitions? What is his birthday?
> #George E. Andrews
> #1938/12/4
> 
> #Attendence Q5.
> #What is the a number of this sequence? 
> seq(nops(PnD(i,1)),i=1..10);
1, 1, 2, 2, 3, 4, 5, 6, 8, 10
> #A000009: 	Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts.
> 
> #Attendence Q6.
> seq(nops(PnD(i,2)),i=1..20);
1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 14, 17, 19, 23, 26, 31
> #A3114:Number of partitions of n into parts 5k+1 or 5k+4.
> 
> #Attendence Q7.
> #Whoses theorem is it that these above two sequences are the same? 
> #	G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109, 238.
> 
> #Attendence Q8.
> #What is the a number of this sequence? 
> seq(pn(5*n+4)/5, n=1..20);
6, 27, 98, 315, 913, 2462, 6237, 15035, 34705, 77231, 166364, 348326, 710869, 1417900, 2769730, 5308732, 9999185, 18533944, 33845975, 60960273
> #A071734: 		a(n) = p(5n+4)/5 where p(k) denotes the k-th partition number.
> 
> #Attendence Q9.
> #Does there exist a k between 0 and 6 such that
> seq(pn(7*n+5)/7, n=1..20);
11, 70, 348, 1449, 5334, 17822, 55165, 160215, 441105, 1159752, 2929465, 7142275, 16873472, 38749850, 86737678, 189672868, 405991500, 852077072, 1756048833, 3558408287
> #A071746: 	a(n) = p(7n+5)/7 where p(k) denotes the k-th partition number.
> 
> Does there exist a k between 0 and 10 such that
> seq(pn(11*n+6)/11, n=1..20);
27, 338, 2835, 18566, 101955, 490253, 2121679, 8424520, 31120519, 108082568, 355805845, 1117485621, 3366123200, 9767105406, 27398618368, 74534264393, 197147918679, 508189847045, 1279140518117, 3149375120229
> #A076394: 		a(n) = p(11n+6)/11 where p(n) = number of partitions of n (A000041).
> 
> #Attendence Q10.
> #Why should Dr.Z from now on make you watch the lectures before the recitation? 
> #So that, we can ask questions for the lecture during the recitation.  
> 
> 
>