O16-C046
> restart;
> u:=n->sin(Pi*((2+sqrt(3))^n));

                                                 n
                   u := n -> sin(Pi (2 + sqrt(3)) )

> seq(simplify((2+sqrt(3))^n+(2-sqrt(3))^n),n=5..30);#(2+sqrt(3))^n+(2-sqrt(3))^n) est un entier pair

  724, 2702, 10084, 37634, 140452, 524174, 1956244, 7300802, 27246964,

        101687054, 379501252, 1416317954, 5285770564, 19726764302,

        73621286644, 274758382274, 1025412242452, 3826890587534,

        14282150107684, 53301709843202, 198924689265124,

        742397047217294, 2770663499604052, 10340256951198914,

        38590364305191604, 144021200269567502

> seq(evalf(u(n)),n=0..30):
> s:=array(0..30):s[0]:=0:for k from 1 to 30 do s[k]:=s[k-1]+u(k) od:seq(evalf(s[n]),n=0..30):
> # sin((2-sqrt(3))^n)) est le TG d'une série CV (équiv. à une géométrique CV)
>