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Av(132, 213, 231, 312, 1234)

Permutation examples

length 2: 12, 21

length 3: 123, 321

length 4: 4321

length 5: 54321

Generating function

$A(x) = \frac{x^{4} - x^{2} - 1}{x - 1}$

Coefficients

1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, ...

System of equations

$\operatorname{F_{4}}{\left (x \right )} = \operatorname{F_{0}}{\left (x \right )} + \operatorname{F_{3}}{\left (x \right )}$

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

$\operatorname{F_{3}}{\left (x \right )} = \operatorname{F_{1}}{\left (x \right )} + \operatorname{F_{2}}{\left (x \right )}$

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

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