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Av(132, 2341, 3214, 3241, 3412, 3421)

Permutation examples

length 2: 12, 21

length 3: 123, 213, 231, 312, 321

length 4: 1234, 2134, 2314, 3124, 4123, 4213, 4231, 4312, 4321

length 5: 12345, 21345, 23145, 31245, 41235, 51234, 52134, 52314, 53124, 54123, 54213, 54231, 54312, 54321

ATRAP tree (size 5, depth 3)

Legend

$\mathcal{A}$ = Av(132, 2341, 3214, 3241, 3412, 3421)

$\mathcal{B}$ = Av(21)

$\mathcal{C}$ = Av(123, 132, 213, 231)

$\mathcal{D}$ = Av(132, 321, 2341, 3412)

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

Generating function

$A(x) = \frac{x^{4} - x^{3} - 2 x^{2} + 2 x - 1}{x^{3} - 3 x^{2} + 3 x - 1}$

Coefficients

1, 1, 2, 5, 9, 14, 20, 27, 35, 44, 54, ...

System of equations

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

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

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

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

$\operatorname{F_{2}}{\left (x \right )} = - \frac{x}{x - 1} \left(-1 + \frac{- x^{4} + x^{3} + x^{2} - x + 1}{x^{2} - 2 x + 1}\right)$