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 A317109 #37 Dec 31 2020 11:11:15 %S A317109 0,4,8,14,20,26,34,40,48,58,68,74,84,90,100,114,126,132,144,150,162, %T A317109 178,188,194,208,220,230,246,262,268,284,290,306,322,332,346,364,370, %U A317109 380,396,414,420,438,444,462,484,494,500,520,534,556,572,590,596,616,636 %N A317109 a(n) is the total number of edges after n-th stage in the diagram of the symmetries of sigma described in A236104, with a(0) = 0. %C A317109 All terms are even numbers. %C A317109 Note that the two-dimensional diagram is also the top view of the stepped pyramid with n levels described in A245092. %C A317109 For the construction of the two-dimensional diagram using Dyck paths and for more information about the pyramid see A237593. %H A317109 Robert Price, <a href="/A317109/b317109.txt">Table of n, a(n) for n = 0..5000</a> %F A317109 a(n) = A294723(n) + A237590(n) - 1 (Euler's formula). %e A317109 Illustration of initial terms (n = 1..9): %e A317109 . _ _ _ _ %e A317109 . _ _ _ |_ _ _ |_ %e A317109 . _ _ _ |_ _ _| |_ _ _| |_ %e A317109 . _ _ |_ _ |_ |_ _ |_ _ |_ _ |_ _ | %e A317109 . _ _ |_ _|_ |_ _|_ | |_ _|_ | | |_ _|_ | | | %e A317109 . _ |_ | |_ | | |_ | | | |_ | | | | |_ | | | | | %e A317109 . |_| |_|_| |_|_|_| |_|_|_|_| |_|_|_|_|_| |_|_|_|_|_|_| %e A317109 . %e A317109 . 4 8 14 20 26 34 %e A317109 . %e A317109 . _ _ _ _ _ %e A317109 . _ _ _ _ _ |_ _ _ _ _| %e A317109 . _ _ _ _ |_ _ _ _ | |_ _ _ _ |_ _ %e A317109 . |_ _ _ _| |_ _ _ _| |_ |_ _ _ _| |_ | %e A317109 . |_ _ _ |_ |_ _ _ |_ |_ _ |_ _ _ |_ |_|_ _ %e A317109 . |_ _ _| |_ _ |_ _ _| |_ _ | |_ _ _| |_ _ | | %e A317109 . |_ _ |_ _ | | |_ _ |_ _ | | | |_ _ |_ _ | | | | %e A317109 . |_ _|_ | | | | |_ _|_ | | | | | |_ _|_ | | | | | | %e A317109 . |_ | | | | | | |_ | | | | | | | |_ | | | | | | | | %e A317109 . |_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_| %e A317109 . %e A317109 . 40 48 58 %e A317109 . %e A317109 . %e A317109 Illustration of the diagram after 29 stages (contain 268 edges, 215 vertices and 54 regions or parts): %e A317109 ._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ %e A317109 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| %e A317109 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ | %e A317109 |_ _ _ _ _ _ _ _ _ _ _ _ _ _| | %e A317109 |_ _ _ _ _ _ _ _ _ _ _ _ _ | | %e A317109 |_ _ _ _ _ _ _ _ _ _ _ _ _| | | %e A317109 |_ _ _ _ _ _ _ _ _ _ _ _ | | |_ _ _ %e A317109 |_ _ _ _ _ _ _ _ _ _ _ _| | |_ _ _ | %e A317109 |_ _ _ _ _ _ _ _ _ _ _ | | |_ _ | |_ %e A317109 |_ _ _ _ _ _ _ _ _ _ _| | |_ _ _| |_ |_ %e A317109 |_ _ _ _ _ _ _ _ _ _ | | |_ _| |_ %e A317109 |_ _ _ _ _ _ _ _ _ _| | |_ _ |_ |_ _ |_ _ %e A317109 |_ _ _ _ _ _ _ _ _ | |_ _ _| |_ | |_ _ | %e A317109 |_ _ _ _ _ _ _ _ _| | |_ _ |_ |_|_ _ | | %e A317109 |_ _ _ _ _ _ _ _ | |_ _ |_ _|_ | | | |_ _ _ _ _ _ %e A317109 |_ _ _ _ _ _ _ _| | | | |_ _ | |_|_ _ _ _ _ | | %e A317109 |_ _ _ _ _ _ _ | |_ _ |_ |_ | | |_ _ _ _ _ | | | | %e A317109 |_ _ _ _ _ _ _| |_ _ |_ |_ _ | | |_ _ _ _ _ | | | | | | %e A317109 |_ _ _ _ _ _ | |_ |_ |_ | |_|_ _ _ _ | | | | | | | | %e A317109 |_ _ _ _ _ _| |_ _| |_ | |_ _ _ _ | | | | | | | | | | %e A317109 |_ _ _ _ _ | |_ _ | |_ _ _ _ | | | | | | | | | | | | %e A317109 |_ _ _ _ _| |_ | |_|_ _ _ | | | | | | | | | | | | | | %e A317109 |_ _ _ _ |_ _|_ |_ _ _ | | | | | | | | | | | | | | | | %e A317109 |_ _ _ _| |_ | |_ _ _ | | | | | | | | | | | | | | | | | | %e A317109 |_ _ _ |_ |_|_ _ | | | | | | | | | | | | | | | | | | | | %e A317109 |_ _ _| |_ _ | | | | | | | | | | | | | | | | | | | | | | %e A317109 |_ _ |_ _ | | | | | | | | | | | | | | | | | | | | | | | | %e A317109 |_ _|_ | | | | | | | | | | | | | | | | | | | | | | | | | | %e A317109 |_ | | | | | | | | | | | | | | | | | | | | | | | | | | | | %e A317109 |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| %e A317109 . %Y A317109 Cf. A294723 (number of vertices). %Y A317109 Cf. A237590 (number of regions or parts). %Y A317109 Compare with A317292 (analog for the diagram that contains subparts). %Y A317109 Cf. A000203, A024916, A196020, A235791, A236104, A237048, A237270, A237271, A237591, A237593, A245092, A262626, A296508. %K A317109 nonn %O A317109 0,2 %A A317109 _Omar E. Pol_, Jul 21 2018 %E A317109 More terms and b-file from _Robert Price_, Jul 31 2018