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Av(132, 231)

Permutation examples

length 2: 12, 21

length 3: 123, 213, 312, 321

length 4: 1234, 2134, 3124, 3214, 4123, 4213, 4312, 4321

length 5: 12345, 21345, 31245, 32145, 41235, 42135, 43125, 43215, 51234, 52134, 53124, 53214, 54123, 54213, 54312, 54321

ATRAP tree (size 3, depth 2)

Legend

$\mathcal{A}$ = Av(132, 231)

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

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

Generating function

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

Coefficients

1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ...

System of equations

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

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

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