Attention! You have been redirected to a symmetry.

Av(132, 213, 231)

Permutation examples

length 2: 12, 21

length 3: 123, 312, 321

length 4: 1234, 4123, 4312, 4321

length 5: 12345, 51234, 54123, 54312, 54321

Generating function

$A(x) = \frac{x^{2} - x + 1}{x^{2} - 2 x + 1}$

Coefficients

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...

System of equations

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

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

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