Av(12)

Permutation examples

length 2: 21

length 3: 321

length 4: 4321

length 5: 54321

ATRAP tree (size 3, depth 2)

Legend

$\mathcal{A}$ = Av(12)

Generating function

$A(x) = - \frac{1}{x - 1}$

Coefficients

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

System of equations

$\operatorname{F_{2}}{\left (x \right )} = \operatorname{F_{0}}{\left (x \right )} + \operatorname{F_{1}}{\left (x \right )}$

$\operatorname{F_{0}}{\left (x \right )} = 1$

$\operatorname{F_{1}}{\left (x \right )} = x \operatorname{F_{2}}{\left (x \right )}$