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 A244370 #24 Oct 20 2014 02:32:31 %S A244370 8,24,48,80,112,160,200,264,328,408,464,560,624,728,832,960,1040,1184, %T A244370 1272,1432,1576,1728,1832,2024,2160,2336,2512,2736 %N A244370 Total number of toothpicks after n-th stage in the toothpick structure of the symmetric representation of sigma in the four quadrants. %C A244370 Partial sums of A244371. %C A244370 If we use toothpicks of length 1/2, so the area of the central square is equal to 1. The total area of the structure after n-th stage is equal to A024916(n), the sum of all divisors of all positive integers <= n, hence the total area of the n-th set of symmetric regions added at n-th stage is equal to sigma(n) = A000203(n), the sum of divisors of n. %C A244370 If we use toothpicks of length 1, so the number of cells (and the area) of the central square is equal to 4. The number of cells (and the total area) of the structure after n-th stage is equal to 4*A024916(n) = A243980(n), hence the number of cells (and the total area) of the n-th set of symmetric regions added at n-th stage is equal to 4*A000203(n) = A239050(n). %F A244370 a(n) = 4*A244362(n) = 8*A244360(n). %e A244370 Illustration of the structure after 16 stages (Contains 960 toothpicks): %e A244370 . %e A244370 . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ %e A244370 . | _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ | %e A244370 . | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | %e A244370 . _ _| | _ _ _ _ _ _ _ _ _ _ _ _ _ _ | |_ _ %e A244370 . _| _ _| |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |_ _ |_ %e A244370 . _| _| _| | _ _ _ _ _ _ _ _ _ _ _ _ | |_ |_ |_ %e A244370 . | _| |_ _| |_ _ _ _ _ _ _ _ _ _ _ _| |_ _| |_ | %e A244370 . _ _ _| | _ _| | _ _ _ _ _ _ _ _ _ _ | |_ _ | |_ _ _ %e A244370 . | _ _ _|_| | _| |_ _ _ _ _ _ _ _ _ _| |_ | |_|_ _ _ | %e A244370 . | | | _ _ _| _|_ _| _ _ _ _ _ _ _ _ |_ _|_ |_ _ _ | | | %e A244370 . | | | | | _ _ _| | _| |_ _ _ _ _ _ _ _| |_ | |_ _ _ | | | | | %e A244370 . | | | | | | | _ _|_| _| _ _ _ _ _ _ |_ |_|_ _ | | | | | | | %e A244370 . | | | | | | | | | _ _| |_ _ _ _ _ _| |_ _ | | | | | | | | | %e A244370 . | | | | | | | | | | | _ _| _ _ _ _ |_ _ | | | | | | | | | | | %e A244370 . | | | | | | | | | | | | | _|_ _ _ _|_ | | | | | | | | | | | | | %e A244370 . | | | | | | | | | | | | | | | _ _ | | | | | | | | | | | | | | | %e A244370 . | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | %e A244370 . | | | | | | | | | | | | | | | |_ _| | | | | | | | | | | | | | | | %e A244370 . | | | | | | | | | | | | | |_|_ _ _ _|_| | | | | | | | | | | | | | %e A244370 . | | | | | | | | | | | |_|_ |_ _ _ _| _|_| | | | | | | | | | | | %e A244370 . | | | | | | | | | |_|_ |_ _ _ _ _ _| _|_| | | | | | | | | | %e A244370 . | | | | | | | |_|_ _ |_ |_ _ _ _ _ _| _| _ _|_| | | | | | | | %e A244370 . | | | | | |_|_ _ | |_ |_ _ _ _ _ _ _ _| _| | _ _|_| | | | | | %e A244370 . | | | |_|_ _ |_|_ _| |_ _ _ _ _ _ _ _| |_ _|_| _ _|_| | | | %e A244370 . | |_|_ _ _ | |_ |_ _ _ _ _ _ _ _ _ _| _| | _ _ _|_| | %e A244370 . |_ _ _ | |_|_ | |_ _ _ _ _ _ _ _ _ _| | _|_| | _ _ _| %e A244370 . | |_ |_ _ |_ _ _ _ _ _ _ _ _ _ _ _| _ _| _| | %e A244370 . |_ |_ |_ | |_ _ _ _ _ _ _ _ _ _ _ _| | _| _| _| %e A244370 . |_ |_ _| |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |_ _| _| %e A244370 . |_ _ | |_ _ _ _ _ _ _ _ _ _ _ _ _ _| | _ _| %e A244370 . | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | %e A244370 . | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | %e A244370 . |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| %e A244370 . %Y A244370 Cf. A000203, A004125, A024916, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239050, A239660, A239931-A239934, A243980, A244050, A244360-A244363, A244371, A244970, A244971, A245092. %K A244370 nonn,more %O A244370 1,1 %A A244370 _Omar E. Pol_, Jun 26 2014 %E A244370 a(8) corrected and more terms from _Omar E. Pol_, Oct 18 2014