Lattice paths count

cache = []

def binomial(n, k) {

    if (n == k || k == 0) {
        return 1G
    }

    if (! cache[n]) {
        cache[n] = []
    }

    if (! cache[n][k]) {
        cache[n][k] = binomial(n-1,k) + binomial(n-1,k-1)
    }

    return cache[n][k]
}

println "Lattice paths counts:"
println "For 2x2 grid there are ${binomial(4,2)} paths"
println "For 3x3 grid there are ${binomial(6,3)} paths"