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 A262611 #36 Dec 30 2018 04:37:57 %S A262611 1,1,2,1,1,2,2,2,1,1,2,3,3,3,2,1,1,2,3,3,3,3,3,2,1,1,2,3,4,4,5,4,4,3, %T A262611 2,1,1,2,3,4,4,4,5,4,4,4,3,2,1,1,2,3,4,5,5,5,6,5,5,5,4,3,2,1,1,2,3,4, %U A262611 5,5,5,6,7,6,5,5,5,4,3,2,1,1,2,3,4,5,6,6,6,7,7,7,6,6,6,5,4,3,2,1,1,2,3,4,5,6,6,6,6,7,7,7,6,6,6,6,5,4,3,2,1 %N A262611 Triangle read by rows in which row n lists the widths of the symmetric representation of A024916(n): the sum of all divisors of all positive integers <= n. %C A262611 Here T(n,k) is defined to be the "k-th width" of the symmetric representation of A024916(n), with n>=1 and 1<=k<=2n-1. %C A262611 If both A249351 and this sequence are written as isosceles triangles then the partial sums of the columns of A249351 give the columns of this isosceles triangle (see the second triangle in Example section). %C A262611 For the definition of the k-th width of the symmetric representation of sigma(n) see A249351. %C A262611 Note that for the geometric representation of the n-th row of the triangle we need the x-axis, the y-axis, and only a Dyck path which is given by the elements of the n-th row of the triangle A237593. %C A262611 Row n has length 2*n-1. %C A262611 Row sums give A024916. %C A262611 The middle diagonal is A240542. %e A262611 Triangle begins: %e A262611 1; %e A262611 1,2,1; %e A262611 1,2,2,2,1; %e A262611 1,2,3,3,3,2,1; %e A262611 1,2,3,3,3,3,3,2,1; %e A262611 1,2,3,4,4,5,4,4,3,2,1; %e A262611 1,2,3,4,4,4,5,4,4,4,3,2,1; %e A262611 1,2,3,4,5,5,5,6,5,5,5,4,3,2,1; %e A262611 1,2,3,4,5,5,5,6,7,6,5,5,5,4,3,2,1; %e A262611 1,2,3,4,5,6,6,6,7,7,7,6,6,6,5,4,3,2,1; %e A262611 1,2,3,4,5,6,6,6,6,7,7,7,6,6,6,6,5,4,3,2,1; %e A262611 1,2,3,4,5,6,7,7,7,8,9,9,9,8,7,7,7,6,5,4,3,2,1; %e A262611 ... %e A262611 -------------------------------------------------------------------------- %e A262611 . Written as an isosceles triangle %e A262611 . the sequence begins: Diagram for n = 1..12 %e A262611 -------------------------------------------------------------------------- %e A262611 . _ _ _ _ _ _ _ _ _ _ _ _ %e A262611 . 1; |_| | | | | | | | | | | | %e A262611 . 1,2,1; |_ _|_| | | | | | | | | | %e A262611 . 1,2,2,2,1; |_ _| _|_| | | | | | | | %e A262611 . 1,2,3,3,3,2,1; |_ _ _| _|_| | | | | | %e A262611 . 1,2,3,3,3,3,3,2,1; |_ _ _| _| _ _|_| | | | %e A262611 . 1,2,3,4,4,5,4,4,3,2,1; |_ _ _ _| _| | _ _|_| | %e A262611 . 1,2,3,4,4,4,5,4,4,4,3,2,1; |_ _ _ _| |_ _|_| _ _| %e A262611 . 1,2,3,4,5,5,5,6,5,5,5,4,3,2,1; |_ _ _ _ _| _| | %e A262611 . 1,2,3,4,5,5,5,6,7,6,5,5,5,4,3,2,1; |_ _ _ _ _| | _| %e A262611 . 1,2,3,4,5,6,6,6,7,7,7,6,6,6,5,4,3,2,1; |_ _ _ _ _ _| _ _| %e A262611 . 1,2,3,4,5,6,6,6,6,7,7,7,6,6,6,6,5,4,3,2,1; |_ _ _ _ _ _| | %e A262611 .1,2,3,4,5,6,7,7,7,8,9,9,9,8,7,7,7,6,5,4,3,2,1; |_ _ _ _ _ _ _| %e A262611 ... %e A262611 For n = 3 the symmetric representation of A024916(3) = 8 in the 4th quadrant looks like this: %e A262611 . %e A262611 . Polygon Cells %e A262611 . _ _ _ _ _ _ %e A262611 . | | |_|_|_| %e A262611 . | _| |_|_|_| %e A262611 . |_ _| |_|_| %e A262611 . %e A262611 There are eight cells. The representation of the widths looks like this: %e A262611 . %e A262611 . \ \ \ %e A262611 . \ \ \ %e A262611 . \ \ 1 %e A262611 . 2 2 %e A262611 . 1 2 %e A262611 . %e A262611 So the third row of the triangle is [1, 2, 2, 2, 1]. %Y A262611 Cf. A024916, A236104, A237048, A237593, A240542, A241008, A241010, A244250, A245685, A246955, A247687, A249351, A250068, A250070, A250071, A253258, A262626. %K A262611 nonn,tabf %O A262611 1,3 %A A262611 _Omar E. Pol_, Sep 26 2015