[math-fun] Fibonacci, cosh, sinh

It is well-known that fib(n) = cosh(n*alpha)/cosh(alpha) (n odd) fib(n) = sinh(n*alpha)/cosh(alpha) (n even) alpha = asinh(1/2). Also, fib(n) = phi^n-(-phi)^(-n) ----------------- sqrt(5) Is there any version of these equations fib(n) = A*exp(a*n)+B*exp(b*n)+C*exp(c*n)+... that *doesn't* require splitting up into n odd, n even? (I'm willing to accept complex A,a,B,b,C,c, etc.)