n

k

1

1

$c_1^{\left(1\right)}=\frac{1}{6}{c}_1^{\left(0\right)}=\frac{1}{6}\frac{1}{2}=\frac{1}{12}$

2

$c_2^{\left(1\right)}=\frac{1}{2}-c_1^{\left(1\right)}=\frac{1}{2}-\frac{1}{12}=\frac{5}{12}$

2

1

$c_1^{\left(2\right)}=\frac{1}{6}{c}_1^{\left(1\right)}=\frac{1}{6}\frac{1}{12}=\frac{1}{72}$

2

$c_2^{\left(2\right)}=\frac{1}{6}{c}_2^{\left(1\right)}=\frac{1}{6}\frac{5}{12}=\frac{5}{72}$

3

$c_3^{\left(2\right)}=\frac{1}{2^2}-c_2^{\left(2\right)}=\frac{1}{4}-\frac{5}{72}=\frac{13}{72}$

4

$c_4^{\left(2\right)}=\frac{1}{2^2}-c_1^{\left(2\right)}=\frac{1}{4}-\frac{1}{72}=\frac{17}{72}$

3

1

$c_1^{\left(3\right)}=\frac{1}{6}{c}_1^{\left(2\right)}=\frac{1}{6}\frac{1}{72}=\frac{1}{432}$

2

$c_2^{\left(3\right)}=\frac{1}{6}{c}_2^{\left(2\right)}=\frac{1}{6}\frac{5}{72}=\frac{5}{432}$

3

$c_3^{\left(3\right)}=\frac{1}{6}{c}_3^{\left(2\right)}=\frac{1}{6}\frac{13}{72}=\frac{13}{432}$

4

$c_4^{\left(3\right)}=\frac{1}{6}{c}_4^{\left(2\right)}=\frac{1}{6}\frac{17}{12}=\frac{17}{432}$

5

$c_5^{\left(3\right)}=\frac{1}{2^3}-c_4^{\left(3\right)}=\frac{1}{8}-\frac{17}{432}=\frac{37}{432}$

6

$c_6^{\left(3\right)}=\frac{1}{2^3}-c_3^{\left(3\right)}=\frac{1}{8}-\frac{13}{432}=\frac{41}{432}$

7

$c_7^{\left(3\right)}=\frac{1}{2^3}-c_2^{\left(3\right)}=\frac{1}{8}-\frac{5}{432}=\frac{49}{432}$

8

$c_8^{\left(3\right)}=\frac{1}{2^3}-c_1^{\left(3\right)}=\frac{1}{8}-\frac{1}{432}=\frac{53}{432}$