Av(132, 1234, 2314, 2341, 3124, 3241, 3412, 3421, 4123, 4213, 4231)
View Raw Data
Generating Function
x43x3x21x1
Counting Sequence
1, 1, 2, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, ...
Implicit Equation for the Generating Function
(1x)F(x)+x43x3x21=0
Recurrence
a(0)=1
a(1)=1
a(2)=2
a(3)=5
a(4)=4
a(n)=4,n5
Explicit Closed Form
{1n=0 or n=12n=25n=34otherwise

This specification was found using the strategy pack "Point Placements" and has 23 rules.

Found on January 18, 2022.

Finding the specification took 0 seconds.

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Created with Raphaël 2.1.4
22, 4
4
x
21
20, 17
2
1
2
1
19, 7
1
1
+
18
2
1
4
x
17
2
1
16
1
+
15
2
1
14, 11
1
1
9
+
13
1
4
x
11, 12
1
1
+
10
2
1
4
1
+
9
4
x
7, 8
1
1
+
6
1
+
5
2
1
4
x
2, 3
1
2
1
1
+
0
1

Copy 23 equations to clipboard:
F0(x)=F1(x)+F2(x)F1(x)=1F2(x)=F3(x)F3(x)=F4(x)F5(x)F4(x)=xF5(x)=F10(x)+F6(x)F6(x)=F1(x)+F7(x)F7(x)=F8(x)F8(x)=F4(x)F9(x)F9(x)=F1(x)+F4(x)F10(x)=F11(x)+F15(x)F11(x)=F12(x)F12(x)=F13(x)F4(x)F13(x)=F14(x)+F9(x)F14(x)=F11(x)F15(x)=F16(x)+F17(x)+F21(x)F16(x)=0F17(x)=F18(x)F4(x)F18(x)=F19(x)+F20(x)F19(x)=F7(x)F20(x)=F17(x)F21(x)=F22(x)F4(x)F22(x)=F4(x)