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# Name:Treasa Bency Biju Jose
# Date: 10-30-2020
# Assignment #16
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1.
with*GroupTheory;
p_3 := proc(n) local i, t, c, s, j; 
c := 0; 
t := nops(permute(n)); 
s := seq(Perm(permute(n)[j]), j = 1 .. t); 
for i to t do 
   if PermOrder(s[i]) <= 3 then 
      c := c + 1; 
   end if; 
end do; 
c; 
end proc;

t:=[seq(p_3(n),n=2..7];
                 t := [2, 6, 18, 46, 156, 582]

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3.
S6 := proc(n) local i, s, k; i := seq(binomial(n, k)^6, k = 0 .. n); end proc;

S6sum := proc(n) local i; i := sum(binomial(n, k)^6, k = 0 .. n); end proc;
S6sum(3);
                              1460

S6seq := proc(n, N) local i, t, l; l := []; t := S6(n); for i to N do l := [op(l), t[i]]; end do; end proc;

time(S6seq(1000, 1000));
                             0.015
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