This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A340846 #33 Oct 28 2021 20:18:35 %S A340846 4,6,8,10,10,12,12,14,16,16,14,18,14,18,22,22,16,22,16,22,26,22,18,26, %T A340846 24,22,28,28,20,30,20,30,30,24,28,32,22,26,32,34,22,34,22,34,38,28,24, %U A340846 38,32,40,34,36,24,38,38,42,36,30,26,42,26,30,46,42,40,44,28 %N A340846 a(n) is the number of edges in the diagram of the symmetric representation of sigma(n). %C A340846 Since the diagram is symmetric so all terms are even numbers. %C A340846 For another version with subparts see A340848 from which first differs at a(6). %F A340846 a(n) = A340833(n) + A237271(n) - 1 (Euler's formula). %e A340846 Illustration of initial terms: %e A340846 . _ _ _ _ %e A340846 . _ _ _ |_ _ _ |_ %e A340846 . _ _ _ |_ _ _| | |_ %e A340846 . _ _ |_ _ |_ |_ _ |_ _ | %e A340846 . _ _ |_ _|_ |_ | | | | | %e A340846 . _ |_ | | | | | | | | | %e A340846 . |_| |_| |_| |_| |_| |_| %e A340846 . %e A340846 n: 1 2 3 4 5 6 %e A340846 a(n): 4 6 8 10 10 12 %e A340846 . %e A340846 For n = 6 the diagram has 12 edges so a(6) = 12. %e A340846 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. %e A340846 . _ _ _ _ _ %e A340846 . _ _ _ _ _ |_ _ _ _ _| %e A340846 . _ _ _ _ |_ _ _ _ | |_ _ %e A340846 . |_ _ _ _| | |_ |_ | %e A340846 . |_ |_ |_ _ |_|_ _ %e A340846 . |_ _ |_ _ | | | %e A340846 . | | | | | | %e A340846 . | | | | | | %e A340846 . | | | | | | %e A340846 . |_| |_| |_| %e A340846 . %e A340846 n: 7 8 9 %e A340846 a(n): 12 14 16 %e A340846 . %e A340846 For n = 9 the diagram has 16 edges so a(9) = 16. %e A340846 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. %e A340846 Another way for the illustration of initial terms is as follows: %e A340846 -------------------------------------------------------------------------- %e A340846 . n a(n) Diagram %e A340846 -------------------------------------------------------------------------- %e A340846 _ %e A340846 1 4 |_| _ %e A340846 _| | _ %e A340846 2 6 |_ _| | | _ %e A340846 _ _|_| | | _ %e A340846 3 8 |_ _| _| | | | _ %e A340846 _ _| _| | | | | _ %e A340846 4 10 |_ _ _| _|_| | | | | _ %e A340846 _ _ _| _ _| | | | | | _ %e A340846 5 10 |_ _ _| | _| | | | | | | _ %e A340846 _ _ _| _| _|_| | | | | | | _ %e A340846 6 12 |_ _ _ _| _| _ _| | | | | | | | _ %e A340846 _ _ _ _| _| _ _| | | | | | | | | _ %e A340846 7 12 |_ _ _ _| | _| _ _|_| | | | | | | | | _ %e A340846 _ _ _ _| | _| | _ _| | | | | | | | | | _ %e A340846 8 14 |_ _ _ _ _| |_ _| | _ _| | | | | | | | | | | _ %e A340846 _ _ _ _ _| _ _|_| _ _|_| | | | | | | | | | | %e A340846 9 16 |_ _ _ _ _| | _| _| _ _ _| | | | | | | | | | %e A340846 _ _ _ _ _| | _| _| _ _| | | | | | | | | %e A340846 10 16 |_ _ _ _ _ _| | _| | _ _|_| | | | | | | %e A340846 _ _ _ _ _ _| | _| | _ _ _| | | | | | %e A340846 11 14 |_ _ _ _ _ _| | _ _| _| | _ _ _| | | | | %e A340846 _ _ _ _ _ _| | _ _| _|_| _ _ _|_| | | %e A340846 12 18 |_ _ _ _ _ _ _| | _ _| _ _| | _ _ _| | %e A340846 _ _ _ _ _ _ _| | _| | _| | _ _ _| %e A340846 13 14 |_ _ _ _ _ _ _| | | _| _| _| | %e A340846 _ _ _ _ _ _ _| | |_ _| _| _| %e A340846 14 18 |_ _ _ _ _ _ _ _| | _ _| _| %e A340846 _ _ _ _ _ _ _ _| | _ _| %e A340846 15 22 |_ _ _ _ _ _ _ _| | | %e A340846 _ _ _ _ _ _ _ _| | %e A340846 16 22 |_ _ _ _ _ _ _ _ _| %e A340846 ... %Y A340846 Cf. A237271 (number of parts or regions). %Y A340846 Cf. A340833 (number of vertices). %Y A340846 Cf. A340848 (number of edges in the diagram with subparts). %Y A340846 Cf. A317109 (total number of edges in the unified diagram). %Y A340846 Cf. A239931-A239934 (illustration of first 32 diagrams). %Y A340846 Cf. A000203, A005843, A196020, A236104, A235791, A237048, A237270, A237590, A237591, A237593, A239660, A245092, A262626, A340847. %K A340846 nonn %O A340846 1,1 %A A340846 _Omar E. Pol_, Jan 24 2021 %E A340846 More terms from _Omar E. Pol_, Oct 28 2021