project-euler/Sidef/100 Arranged probability -- v2.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 17 February 2017
# License: GPLv3
# https://github.com/trizen

# https://projecteuler.net/problem=100

# Runtime: 0.188s

func a(n) is cached {
    n == 0 && return 0
    n == 1 && return 3
    6*a(n-1) - a(n-2) + 2
}

func b(n) is cached {
    n == 0 && return 1
    n == 1 && return 3
    6*b(n-1) - b(n-2) - 2
}

for n in (1 .. Inf) {
    if (a(n) > 1e12) {
        say b(n)
        break
    }
}