bacovia/t/generalized_fibonacci.sf

#!/usr/bin/ruby

# Runtime: 2.587s

include('../lib/bacovia.sf')

func fibonacci(t, n) {
    var a = Power(n**2 + 4, Fraction(1, 2))
    var b = Fraction(a + Power(Power(a, 2) - 4, Fraction(1, 2)), 2)
    Fraction(Power(b, t) - Power(-b, -t), a)
}

say var a = fibonacci(Symbol('n', 12), 1).simple.pretty
say var b = fibonacci(Symbol('n', 12), Symbol('m')).simple.pretty

assert_eq(a, '((((5^(1/2) + (5 - 4)^(1/2))/2)^n - ((-(5^(1/2) + (5 - 4)^(1/2)))/2)^(-n))/5^(1/2))')
assert_eq(b, '(((((4 + m^2)^(1/2) + ((4 + m^2)^1 - 4)^(1/2))/2)^n - ((-((4 + m^2)^(1/2) + ((4 + m^2)^1 - 4)^(1/2)))/2)^(-n))/(4 + m^2)^(1/2))')