Illustration of initial terms:
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n: 1 2 3 4 5 6
a(n): 4 6 7 10 9 12
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For n = 6 the diagram has 12 vertices so a(6) = 12.
On the other hand the diagram has 12 edges and only one part or region, so applying Euler's formula we have that a(6) = 12 - 1 + 1 = 12.
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n: 7 8 9
a(n): 11 14 14
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For n = 9 the diagram has 14 vertices so a(9) = 14.
On the other hand the diagram has 16 edges and three parts or regions, so applying Euler's formula we have that a(9) = 16 - 3 + 1 = 14.
Another way for the illustration of initial terms is as follows:
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. n a(n) Diagram
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_
1 4 |_| _
_| | _
2 6 |_ _| | | _
_ _|_| | | _
3 7 |_ _| _| | | | _
_ _| _| | | | | _
4 10 |_ _ _| _|_| | | | | _
_ _ _| _ _| | | | | | _
5 9 |_ _ _| | _| | | | | | | _
_ _ _| _| _|_| | | | | | | _
6 12 |_ _ _ _| _| _ _| | | | | | | | _
_ _ _ _| _| _ _| | | | | | | | | _
7 11 |_ _ _ _| | _| _ _|_| | | | | | | | | _
_ _ _ _| | _| | _ _| | | | | | | | | | _
8 14 |_ _ _ _ _| |_ _| | _ _| | | | | | | | | | | _
_ _ _ _ _| _ _|_| _ _|_| | | | | | | | | | |
9 14 |_ _ _ _ _| | _| _| _ _ _| | | | | | | | | |
_ _ _ _ _| | _| _| _ _| | | | | | | | |
10 15 |_ _ _ _ _ _| | _| | _ _|_| | | | | | |
_ _ _ _ _ _| | _| | _ _ _| | | | | |
11 13 |_ _ _ _ _ _| | _ _| _| | _ _ _| | | | |
_ _ _ _ _ _| | _ _| _|_| _ _ _|_| | |
12 18 |_ _ _ _ _ _ _| | _ _| _ _| | _ _ _| |
_ _ _ _ _ _ _| | _| | _| | _ _ _|
13 13 |_ _ _ _ _ _ _| | | _| _| _| |
_ _ _ _ _ _ _| | |_ _| _| _|
14 17 |_ _ _ _ _ _ _ _| | _ _| _|
_ _ _ _ _ _ _ _| | _ _|
15 20 |_ _ _ _ _ _ _ _| | |
_ _ _ _ _ _ _ _| |
16 22 |_ _ _ _ _ _ _ _ _|
...
