Illustration of initial terms:
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n: 1 2 3 4 5 6
a(n): 4 6 8 10 10 14
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For n = 6 the diagram has 14 edges so a(6) = 14.
On the other hand the diagram has 13 vertices and two subparts or regions, so applying Euler's formula we have that a(6) = 13 + 2 - 1 = 14.
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n: 7 8 9
a(n): 12 14 16
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For n = 9 the diagram has 16 edges so a(9) = 16.
On the other hand the diagram has 14 vertices and three subparts or regions, so applying Euler's formula we have that a(9) = 14 + 3 - 1 = 16.
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 8 |_ _| _| | | | _
_ _| _| | | | | _
4 10 |_ _ _| _|_| | | | | _
_ _ _| _ _| | | | | | _
5 10 |_ _ _| | _ _| | | | | | | _
_ _ _| |_| _|_| | | | | | | _
6 14 |_ _ _ _| _| _ _| | | | | | | | _
_ _ _ _| _| _ _| | | | | | | | | _
7 12 |_ _ _ _| | _| _ _|_| | | | | | | | | _
_ _ _ _| | _| | _ _| | | | | | | | | | _
8 14 |_ _ _ _ _| |_ _| | _ _| | | | | | | | | | | _
_ _ _ _ _| _ _|_| _ _|_| | | | | | | | | | |
9 16 |_ _ _ _ _| | _| _| _ _ _| | | | | | | | | |
_ _ _ _ _| | _| _| _ _ _| | | | | | | | |
10 16 |_ _ _ _ _ _| | _| _| | _ _|_| | | | | | |
_ _ _ _ _ _| | _| _| | _ _ _| | | | | |
11 14 |_ _ _ _ _ _| | |_ _| _| | _ _ _| | | | |
_ _ _ _ _ _| | _ _| _|_| _ _ _|_| | |
12 24 |_ _ _ _ _ _ _| | _ _| _ _| | _ _ _| |
_ _ _ _ _ _ _| | _| | _ _| | _ _ _|
13 14 |_ _ _ _ _ _ _| | | _| |_| _| |
_ _ _ _ _ _ _| | |_ _| _| _|
14 18 |_ _ _ _ _ _ _ _| | _ _| _|
_ _ _ _ _ _ _ _| | _ _|
15 24 |_ _ _ _ _ _ _ _| | |
_ _ _ _ _ _ _ _| |
16 22 |_ _ _ _ _ _ _ _ _|
...
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