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 A348705 #41 Dec 18 2021 22:21:05 %S A348705 4,8,12,16,18,24,24,32,34,40,36,48,42,54,56,64,54,72,60,80,78,82,72, %T A348705 96,84,96,98,112,90,120,96,128 %N A348705 a(n) is the total length of all line segments in the symmetric representation of sigma(n). %C A348705 a(n) is also the number of toothpicks of length 1 needed to represent the symmetric representation of sigma(n) (see the examples). %C A348705 The diagram is symmetric thus all terms are even. %C A348705 If the symmetric representation of sigma(n) has only one part (cf. A174973) or if it has two parts and they meet at the center of the Dyck path (cf. A262259) then a(n) = 4*n, otherwise a(n) < 4*n. In other words: if n is a term of A279029 then a(n) = 4*n, otherwise a(n) < 4*n. %F A348705 a(n) = 2*A348854(n). %F A348705 a(n) = A008586(n) - A279228(n). - _Omar E. Pol_, Dec 13 2021 %e A348705 Illustration of initial terms: %e A348705 . _ _ _ _ %e A348705 . _ _ _ |_ _ _ |_ %e A348705 . _ _ _ |_ _ _| | |_ %e A348705 . _ _ |_ _ |_ |_ _ |_ _ | %e A348705 . _ _ |_ _|_ |_ | | | | | %e A348705 . _ |_ | | | | | | | | | %e A348705 . |_| |_| |_| |_| |_| |_| %e A348705 . %e A348705 n: 1 2 3 4 5 6 %e A348705 a(n): 4 8 12 16 18 24 %e A348705 . %e A348705 . _ _ _ _ _ %e A348705 . _ _ _ _ _ |_ _ _ _ _| %e A348705 . _ _ _ _ |_ _ _ _ | |_ _ %e A348705 . |_ _ _ _| | |_ |_ | %e A348705 . |_ |_ |_ _ |_|_ _ %e A348705 . |_ _ |_ _ | | | %e A348705 . | | | | | | %e A348705 . | | | | | | %e A348705 . | | | | | | %e A348705 . |_| |_| |_| %e A348705 . %e A348705 n: 7 8 9 %e A348705 a(n): 24 32 34 %e A348705 . %e A348705 Another way for the illustration of initial terms is as follows: %e A348705 -------------------------------------------------------------------------- %e A348705 . n a(n) Diagram %e A348705 -------------------------------------------------------------------------- %e A348705 _ %e A348705 1 4 |_| _ %e A348705 _| | _ %e A348705 2 8 |_ _| | | _ %e A348705 _ _|_| | | _ %e A348705 3 12 |_ _| _| | | | _ %e A348705 _ _| _| | | | | _ %e A348705 4 16 |_ _ _| _|_| | | | | _ %e A348705 _ _ _| _ _| | | | | | _ %e A348705 5 18 |_ _ _| | _| | | | | | | _ %e A348705 _ _ _| _| _|_| | | | | | | _ %e A348705 6 24 |_ _ _ _| _| _ _| | | | | | | | _ %e A348705 _ _ _ _| _| _ _| | | | | | | | | _ %e A348705 7 24 |_ _ _ _| | _| _ _|_| | | | | | | | | _ %e A348705 _ _ _ _| | _| | _ _| | | | | | | | | | _ %e A348705 8 32 |_ _ _ _ _| |_ _| | _ _| | | | | | | | | | | _ %e A348705 _ _ _ _ _| _ _|_| _ _|_| | | | | | | | | | | %e A348705 9 34 |_ _ _ _ _| | _| _| _ _ _| | | | | | | | | | %e A348705 _ _ _ _ _| | _| _| _ _| | | | | | | | | %e A348705 10 40 |_ _ _ _ _ _| | _| | _ _|_| | | | | | | %e A348705 _ _ _ _ _ _| | _| | _ _ _| | | | | | %e A348705 11 36 |_ _ _ _ _ _| | _ _| _| | _ _ _| | | | | %e A348705 _ _ _ _ _ _| | _ _| _|_| _ _ _|_| | | %e A348705 12 48 |_ _ _ _ _ _ _| | _ _| _ _| | _ _ _| | %e A348705 _ _ _ _ _ _ _| | _| | _| | _ _ _| %e A348705 13 42 |_ _ _ _ _ _ _| | | _| _| _| | %e A348705 _ _ _ _ _ _ _| | |_ _| _| _| %e A348705 14 54 |_ _ _ _ _ _ _ _| | _ _| _| %e A348705 _ _ _ _ _ _ _ _| | _ _| %e A348705 15 56 |_ _ _ _ _ _ _ _| | | %e A348705 _ _ _ _ _ _ _ _| | %e A348705 16 64 |_ _ _ _ _ _ _ _ _| %e A348705 ... %Y A348705 Cf. A008586 (upper bounds). %Y A348705 Cf. A237271 (number of parts or regions). %Y A348705 Cf. A340833 (number of vertices). %Y A348705 Cf. A340846 (number of edges). %Y A348705 Cf. A239931-A239934 (illustration of first 32 diagrams). %Y A348705 Cf. A000203, A139250, A174973, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A238443, A239660, A245092, A262259, A262626, A279029, A279228, A348854. %K A348705 nonn,more %O A348705 1,1 %A A348705 _Omar E. Pol_, Oct 30 2021