Sequences

Sequence
Closed form(ula)
Generating function

{1,1,1,1,...}
a(n)=1
f(x)=1/(1-x)

{1,2,4,8,...}
a(n)=2^n
f(x)=1/(1-2x)

{0,0,0,0,1,1,...}
if (n<4) then a(n)=0 else a(n)=1
f(x)=x^4/(1-x)

See also the Mathematica package RSolve