Av(132, 2341, 3214, 3241, 3412, 4123, 4231, 4312, 4321)
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Generating Function
2x5x43x3x21x1
Counting Sequence
1, 1, 2, 5, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, ...
Implicit Equation for the Generating Function
(1x)F(x)+2x5x43x3x21=0
Recurrence
a(0)=1
a(1)=1
a(2)=2
a(3)=5
a(4)=6
a(5)=4
a(n)=4,n6
Explicit Closed Form
{1n=0 or n=12n=25n=36n=44otherwise

This specification was found using the strategy pack "Point Placements" and has 31 rules.

Found on January 18, 2022.

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F0(x)=F1(x)+F2(x)F1(x)=1F2(x)=F3(x)F3(x)=F4(x)F5(x)F4(x)=xF5(x)=F6(x)+F9(x)F6(x)=F1(x)+F7(x)F7(x)=F8(x)F8(x)=F4(x)F6(x)F9(x)=F10(x)+F17(x)F10(x)=F11(x)F11(x)=F12(x)F4(x)F12(x)=F13(x)+F14(x)F13(x)=F1(x)+F4(x)F14(x)=F15(x)+F4(x)F15(x)=F16(x)F16(x)=x2F17(x)=F18(x)+F19(x)+F24(x)F18(x)=0F19(x)=F20(x)F4(x)F20(x)=F21(x)F21(x)=F22(x)+F7(x)F22(x)=F23(x)F23(x)=F4(x)F7(x)F24(x)=F25(x)F4(x)F25(x)=F26(x)+F28(x)F26(x)=F27(x)F27(x)=F13(x)F4(x)F28(x)=F29(x)F29(x)=F30(x)F4(x)F30(x)=F7(x)