A_n^{\circ}=A_{n-1}^{\circ}+A_{n-1}^{\times}\cdot\frac 1 3+A_{n-1}^{\bullet}\cdot\frac 1 3\cdot\frac 1 4+A_{n-1}^=\cdot\frac 1 3\cdot\frac 1 2=A_{n-1}^{\circ}+\frac 1 3A_{n-1}^{\times}+\frac 1{12}A_{n-1}^{\bullet}+\frac 1 6A_{n-1}^=