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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 Table of n, a(n) for n=1..67. 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). Cf. A000203, A005843, A196020, A236104, A235791, A237048, A237270, A237590, A237591, A237593, A239660, A245092, A262626, A340847. Sequence in context: A087789 A071830 A276982 * A167146 A020891 A340848 Adjacent sequences: A340843 A340844 A340845 * A340847 A340848 A340849 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.)