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 A340848 #34 Feb 03 2021 23:37:04 %S A340848 4,6,8,10,10,14,12,14,16,16,14,24,14,18,24,22,16,28,16,26,26,22,18,36, %T A340848 24,22,28,30,20,44,20,30 %N A340848 a(n) is the number of edges in the diagram of the symmetric representation of sigma(n) with subparts. %C A340848 Since the diagram is symmetric so all terms are even numbers. %C A340848 For another version see A340846 from which first differs at a(6). %C A340848 For the definition of subparts see A279387. For more information about the subparts see also A237271, A280850, A280851, A296508, A335616. %C A340848 Note that in this version of the diagram of the symmetric representation of sigma(n) all regions are called "subparts". The number of subparts equals A001227(n). %F A340848 a(n) = A340847(n) + A001227(n) - 1 (Euler's formula). %e A340848 Illustration of initial terms: %e A340848 . _ _ _ _ %e A340848 . _ _ _ |_ _ _ |_ %e A340848 . _ _ _ |_ _ _| | |_|_ %e A340848 . _ _ |_ _ |_ |_ _ |_ _ | %e A340848 . _ _ |_ _|_ |_ | | | | | %e A340848 . _ |_ | | | | | | | | | %e A340848 . |_| |_| |_| |_| |_| |_| %e A340848 . %e A340848 n: 1 2 3 4 5 6 %e A340848 a(n): 4 6 8 10 10 14 %e A340848 . %e A340848 For n = 6 the diagram has 14 edges so a(6) = 14. %e A340848 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. %e A340848 . _ _ _ _ _ %e A340848 . _ _ _ _ _ |_ _ _ _ _| %e A340848 . _ _ _ _ |_ _ _ _ | |_ _ %e A340848 . |_ _ _ _| | |_ |_ | %e A340848 . |_ |_ |_ _ |_|_ _ %e A340848 . |_ _ |_ _ | | | %e A340848 . | | | | | | %e A340848 . | | | | | | %e A340848 . | | | | | | %e A340848 . |_| |_| |_| %e A340848 . %e A340848 n: 7 8 9 %e A340848 a(n): 12 14 16 %e A340848 . %e A340848 For n = 9 the diagram has 16 edges so a(9) = 16. %e A340848 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. %e A340848 Another way for the illustration of initial terms is as follows: %e A340848 -------------------------------------------------------------------------- %e A340848 . n a(n) Diagram %e A340848 -------------------------------------------------------------------------- %e A340848 _ %e A340848 1 4 |_| _ %e A340848 _| | _ %e A340848 2 6 |_ _| | | _ %e A340848 _ _|_| | | _ %e A340848 3 8 |_ _| _| | | | _ %e A340848 _ _| _| | | | | _ %e A340848 4 10 |_ _ _| _|_| | | | | _ %e A340848 _ _ _| _ _| | | | | | _ %e A340848 5 10 |_ _ _| | _ _| | | | | | | _ %e A340848 _ _ _| |_| _|_| | | | | | | _ %e A340848 6 14 |_ _ _ _| _| _ _| | | | | | | | _ %e A340848 _ _ _ _| _| _ _| | | | | | | | | _ %e A340848 7 12 |_ _ _ _| | _| _ _|_| | | | | | | | | _ %e A340848 _ _ _ _| | _| | _ _| | | | | | | | | | _ %e A340848 8 14 |_ _ _ _ _| |_ _| | _ _| | | | | | | | | | | _ %e A340848 _ _ _ _ _| _ _|_| _ _|_| | | | | | | | | | | %e A340848 9 16 |_ _ _ _ _| | _| _| _ _ _| | | | | | | | | | %e A340848 _ _ _ _ _| | _| _| _ _ _| | | | | | | | | %e A340848 10 16 |_ _ _ _ _ _| | _| _| | _ _|_| | | | | | | %e A340848 _ _ _ _ _ _| | _| _| | _ _ _| | | | | | %e A340848 11 14 |_ _ _ _ _ _| | |_ _| _| | _ _ _| | | | | %e A340848 _ _ _ _ _ _| | _ _| _|_| _ _ _|_| | | %e A340848 12 24 |_ _ _ _ _ _ _| | _ _| _ _| | _ _ _| | %e A340848 _ _ _ _ _ _ _| | _| | _ _| | _ _ _| %e A340848 13 14 |_ _ _ _ _ _ _| | | _| |_| _| | %e A340848 _ _ _ _ _ _ _| | |_ _| _| _| %e A340848 14 18 |_ _ _ _ _ _ _ _| | _ _| _| %e A340848 _ _ _ _ _ _ _ _| | _ _| %e A340848 15 24 |_ _ _ _ _ _ _ _| | | %e A340848 _ _ _ _ _ _ _ _| | %e A340848 16 22 |_ _ _ _ _ _ _ _ _| %e A340848 ... %Y A340848 Cf. A001227 (number of subparts or regions). %Y A340848 Cf. A340847 (number of vertices). %Y A340848 Cf. A340846 (number of edges in the diagram only with parts). %Y A340848 Cf. A317292 (total number of edges in the unified diagram). %Y A340848 Cf. A000203, A060831, A196020, A236104, A235791, A237048, A237270, A237591, A237593, A239660, A245092, A262626, A279387, A280850, A280851, A296508, A335616, A340833. %K A340848 nonn,more %O A340848 1,1 %A A340848 _Omar E. Pol_, Jan 24 2021