int f(int n)
{
   static int r = 0;
   if(n <= 0) return 1;
   if(n>3)
   {
     r = n;
     return f(n-2)+2;
   }
  return f(n-1)+r;
}

The minimum state automation equivalent to the above $$FSA$$ has the following number of states

The language accepted by this automation is given by the regular expression