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 A274919 #31 May 04 2023 10:54:06 %S A274919 4,8,12,16,16,24,20,32,32,40,28,48,32,52,52,64,40,72,44,80,72,76,52, %T A274919 96,68,88,88,112,64,120,68,128 %N A274919 Sum of all perimeters of all parts of the symmetric representation of sigma(n). %C A274919 a(n) is also the number of toothpicks added at n-th stage in the toothpick structure of the symmetric representation of sigma in two quadrants (without the axis x and y). %F A274919 a(n) = 4*A244361(n) = 2*A244363(n) = A244371(n)/2. %F A274919 a(n) = A008586(n) - 2*A279228(n). - _Omar E. Pol_, May 04 2023 %e A274919 Illustration of a(9) = 32: %e A274919 . 12 %e A274919 . _ _ _ _ _ %e A274919 . |_ _ _ _ _| %e A274919 . _ _ 8 %e A274919 . |_ | %e A274919 . |_| _ %e A274919 . | | %e A274919 . | | %e A274919 . | | 12 %e A274919 . | | %e A274919 . |_| %e A274919 . %e A274919 For n = 9 the symmetric representation of sigma(9) = 13 has three parts of areas 5, 3, 5 respectively. The perímeters of the parts are 12, 8 and 12 as shown above. The sum of the perimeters is 12 + 8 + 12 = 32, so a(9) = 32. %Y A274919 Cf. A000203, A008586, A196020, A236104, A237270, A237271, A237593, A244361, A244363, A244370, A244371, A245092, A262626, A279228. %K A274919 nonn,more %O A274919 1,1 %A A274919 _Omar E. Pol_, Dec 11 2016 %E A274919 a(29)-a(32) from _Omar E. Pol_, May 04 2023