[VA] SRC#003- New Year 2019 Special

[Albert Chan]

The idea of only doing only *last* row work for 3x3 matrix too.

Let M = {{k, n, n}, {1, k, n}, {1, 1, k}}

-> M^p = {{c, n*a, n*b},
                 {b,     c, n*a},
                 {a,     b,     c}}, for some a, b, c

-> For M^(p+1), last row = {k*a+b+c, n*a+k*b+c, n*a+n*b+k*c}

Example: this is result of M^200 last row ratios:

Code:

lua> k, n = math.pi, 2019
lua> a, b, c = 1, 1, k
lua> for i=2,200 do
:       a, b, c = (k*a+b+c)/n, a+(k*b+c)/n, a+b+k*c/n
:    end
lua> =a, b, c
2.916424658351884e-212  3.686063969271537e-211  4.658809733574611e-210
lua> =b/a, c/b
12.638982319380704      12.638982319385288