project-euler/Sidef/140 Modified Fibonacci golden nuggets -- v2.sf

#!/usr/bin/ruby

# Author: Daniel "Trizen" Șuteu
# Date: 19 September 2016
# License: GPLv3
# Website: https://github.com/trizen

# https://projecteuler.net/problem=140

# Runtime: 0.143s

func lucas(n) is cached {
    n.is_one ? 1
             : (n.is_zero ? 2
                          : (lucas(n-1) + lucas(n-2)))
}

func fib(n) is cached {
    n.is_one ? 1
             : (n.is_zero ? 0
                          : (fib(n-1) + fib(n-2)))
}

func f_even(n) {        # 2n

    var f1 = fib(n)
    var f2 = fib(n+1)

    f1 * (3*f1 + f2)
}

func f_odd(n) {         # 2n+1

    var f1 = fib(n+1)
    var l1 = lucas(n)

    var f2 = fib(n+2)
    var l2 = lucas(n+1)

    -((f1+l1) * ((3*(f1+l1))/(f2+l2) + 1)) / (f2 + l2) /
            (((f1+l1)**2)/((f2+l2)**2) + ((f1+l1)/(f2+l2)) - 1)
}

var sum = 0

for n in (1..30) {
    if (n.is_even) {
        sum += f_even(n)
    }
    else {
        sum += f_odd(n)
    }
}

say sum