Av(1243, 1342, 1423, 1432, 2143, 2413, 2431, 3142, 3412, 4132, 4231)
View Raw Data
Generating Function
2x53x4+x3+3x23x+1(2x1)(x1)2
Counting Sequence
1, 1, 2, 6, 13, 28, 59, 122, 249, 504, 1015, 2038, 4085, 8180, 16371, ...
Implicit Equation for the Generating Function
(2x1)(x1)2F(x)+2x53x4+x3+3x23x+1=0
Recurrence
a(0)=1
a(1)=1
a(2)=2
a(3)=6
a(4)=13
a(5)=28
a(n+1)=2a(n)2+n,n6
Explicit Closed Form
{1n=0 or n=12n=21+2nnotherwise

This specification was found using the strategy pack "Point Placements" and has 21 rules.

Found on July 23, 2021.

Finding the specification took 2 seconds.

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

Copy 21 equations to clipboard:
F0(x)=F1(x)+F2(x)F1(x)=1F2(x)=F3(x)F3(x)=F13(x)F4(x)F4(x)=F0(x)+F5(x)F5(x)=F6(x)F6(x)=F13(x)F7(x)F7(x)=F16(x)+F8(x)F8(x)=F13(x)+F9(x)F9(x)=F10(x)+F11(x)F10(x)=F1(x)+F11(x)F11(x)=F12(x)F12(x)=F10(x)F13(x)F14(x)F13(x)=xF14(x)=F1(x)+F15(x)F15(x)=F13(x)F14(x)F16(x)=F14(x)F17(x)F17(x)=F18(x)F18(x)=F13(x)F14(x)F19(x)F19(x)=F1(x)+F20(x)F20(x)=F17(x)