Av(132, 2134, 2314, 2341, 3124, 3214, 3421, 4123, 4231, 4312, 4321)
View Raw Data
Generating Function
3x5+x43x3x21x1
Counting Sequence
1, 1, 2, 5, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
Implicit Equation for the Generating Function
(1x)F(x)+3x5+x43x3x21=0
Recurrence
a(0)=1
a(1)=1
a(2)=2
a(3)=5
a(4)=4
a(5)=1
a(n)=1,n6
Explicit Closed Form
{2n=25n=34n=41otherwise

This specification was found using the strategy pack "Point Placements" and has 27 rules.

Found on January 18, 2022.

Finding the specification took 0 seconds.

Copy to clipboard:

View tree on standalone page.

Created with Raphaël 2.1.4
13
4
x
25, 26
/
1
4
x
24
/
1
22, 23
21, 4
+
20
4
x
19
18
1
+
17
/
1
15, 16
4
+
14
4
1
+
13
+
12
4
x
10, 11
1
+
9
/
1
6
/
4
x
7, 8
/
/
1
+
6
/
+
5
/
1
4
x
2, 3
1
/
1
1
+
0
1

Copy 27 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)=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)+F22(x)F21(x)=F4(x)F22(x)=F23(x)F23(x)=x2F24(x)=F25(x)F4(x)F25(x)=F26(x)F26(x)=F13(x)F4(x)