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A340846 a(n) is the number of edges in the diagram of the symmetric representation of sigma(n). 5
4, 6, 8, 10, 10, 12, 12, 14, 16, 16, 14, 18, 14, 18, 22, 22, 16, 22, 16, 22, 26, 22, 18, 26, 24, 22, 28, 28, 20, 30, 20, 30, 30, 24, 28, 32, 22, 26, 32, 34, 22, 34, 22, 34, 38, 28, 24, 38, 32, 40, 34, 36, 24, 38, 38, 42, 36, 30, 26, 42, 26, 30, 46, 42, 40, 44, 28 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Since the diagram is symmetric so all terms are even numbers.
For another version with subparts see A340848 from which first differs at a(6).
LINKS
FORMULA
a(n) = A340833(n) + A237271(n) - 1 (Euler's formula).
EXAMPLE
Illustration of initial terms:
. _ _ _ _
. _ _ _ |_ _ _ |_
. _ _ _ |_ _ _| | |_
. _ _ |_ _ |_ |_ _ |_ _ |
. _ _ |_ _|_ |_ | | | | |
. _ |_ | | | | | | | | |
. |_| |_| |_| |_| |_| |_|
.
n: 1 2 3 4 5 6
a(n): 4 6 8 10 10 12
.
For n = 6 the diagram has 12 edges so a(6) = 12.
On the other hand the diagram has 12 vertices and only one part or region, so applying Euler's formula we have that a(6) = 12 + 1 - 1 = 12.
. _ _ _ _ _
. _ _ _ _ _ |_ _ _ _ _|
. _ _ _ _ |_ _ _ _ | |_ _
. |_ _ _ _| | |_ |_ |
. |_ |_ |_ _ |_|_ _
. |_ _ |_ _ | | |
. | | | | | |
. | | | | | |
. | | | | | |
. |_| |_| |_|
.
n: 7 8 9
a(n): 12 14 16
.
For n = 9 the diagram has 16 edges so a(9) = 16.
On the other hand the diagram has 14 vertices and three parts 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:
--------------------------------------------------------------------------
. n a(n) Diagram
--------------------------------------------------------------------------
_
1 4 |_| _
_| | _
2 6 |_ _| | | _
_ _|_| | | _
3 8 |_ _| _| | | | _
_ _| _| | | | | _
4 10 |_ _ _| _|_| | | | | _
_ _ _| _ _| | | | | | _
5 10 |_ _ _| | _| | | | | | | _
_ _ _| _| _|_| | | | | | | _
6 12 |_ _ _ _| _| _ _| | | | | | | | _
_ _ _ _| _| _ _| | | | | | | | | _
7 12 |_ _ _ _| | _| _ _|_| | | | | | | | | _
_ _ _ _| | _| | _ _| | | | | | | | | | _
8 14 |_ _ _ _ _| |_ _| | _ _| | | | | | | | | | | _
_ _ _ _ _| _ _|_| _ _|_| | | | | | | | | | |
9 16 |_ _ _ _ _| | _| _| _ _ _| | | | | | | | | |
_ _ _ _ _| | _| _| _ _| | | | | | | | |
10 16 |_ _ _ _ _ _| | _| | _ _|_| | | | | | |
_ _ _ _ _ _| | _| | _ _ _| | | | | |
11 14 |_ _ _ _ _ _| | _ _| _| | _ _ _| | | | |
_ _ _ _ _ _| | _ _| _|_| _ _ _|_| | |
12 18 |_ _ _ _ _ _ _| | _ _| _ _| | _ _ _| |
_ _ _ _ _ _ _| | _| | _| | _ _ _|
13 14 |_ _ _ _ _ _ _| | | _| _| _| |
_ _ _ _ _ _ _| | |_ _| _| _|
14 18 |_ _ _ _ _ _ _ _| | _ _| _|
_ _ _ _ _ _ _ _| | _ _|
15 22 |_ _ _ _ _ _ _ _| | |
_ _ _ _ _ _ _ _| |
16 22 |_ _ _ _ _ _ _ _ _|
...
CROSSREFS
Cf. A237271 (number of parts or regions).
Cf. A340833 (number of vertices).
Cf. A340848 (number of edges in the diagram with subparts).
Cf. A317109 (total number of edges in the unified diagram).
Cf. A239931-A239934 (illustration of first 32 diagrams).
Sequence in context: A087789 A071830 A276982 * A167146 A020891 A340848
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jan 24 2021
EXTENSIONS
More terms from Omar E. Pol, Oct 28 2021
STATUS
approved

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Last modified May 28 19:24 EDT 2024. Contains 372919 sequences. (Running on oeis4.)