#Please do not post homework
#Ravali Bommanaboina 11/1/20, Assignment 16
#Question 1
p_3:=proc(N) local n,i,seq:
n:=N:
i:=0:
seq:=[]:
for i from 0 to n do
seq:=[op(seq),(binomial(n,i))^6]:
od:
return(seq):
end:


S6seqClever:=proc(ope,n,N,Ini,K)
local ope1,gu,L,n1,j1:
ope1:=Yafe(ope,N)[2]:
L:=degree(ope1,N):
return(S6seq(n)):
if nops(Ini)<>L then
 ERROR(`Ini should be of length`, L):
fi:

ope1:=expand(subs(n=n-L,ope1)/N^L):

gu:=Ini:

for n1 from nops(Ini)+1 to K do
gu:=[op(gu), -add(gu[nops(gu)+1-j1]*subs(n=n1,coeff(ope1,N,-j1)),
j1=1..L)]:
od:

gu:

end:
#Question 3
S6:=proc(n) local i,sum:
i:=0:
sum:=0:
for i from 0 to n do
sum:=(binomial(n,i))^6+sum:
od:
return(sum):
end:

S6seq:=proc(N) local n,i,seq:
n:=N:
i:=0:
seq:=[]:
for i from 0 to n do
seq:=[op(seq),(binomial(n,i))^6]:
od:
return(seq):
end:


S6seqClever:=proc(ope,n,N,Ini,K)
local ope1,gu,L,n1,j1:
ope1:=Yafe(ope,N)[2]:
L:=degree(ope1,N):
return(S6seq(n)):
if nops(Ini)<>L then
 ERROR(`Ini should be of length`, L):
fi:

ope1:=expand(subs(n=n-L,ope1)/N^L):

gu:=Ini:

for n1 from nops(Ini)+1 to K do
gu:=[op(gu), -add(gu[nops(gu)+1-j1]*subs(n=n1,coeff(ope1,N,-j1)),
j1=1..L)]:
od:

gu:

end:

#