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 A240020 #27 Dec 31 2020 11:11:15 %S A240020 1,2,2,3,3,4,4,5,3,5,6,6,7,7,8,8,8,9,9,10,10,11,5,5,11,12,12,13,5,13, %T A240020 14,6,6,14,15,15,16,16,17,7,7,17,18,12,18,19,19,20,8,8,20,21,21,22,22, %U A240020 23,32,23,24,24,25,7,25,26,10,10,26,27,27,28,8,8,28,29,11,11,29,30,30,31,31,32,12,26,12,32,33,9,9,33,34,34 %N A240020 Triangle read by rows in which row n lists the parts of the symmetric representation of sigma(2n-1). %C A240020 Row n lists the parts of the symmetric representation of A008438(n-1). %C A240020 Also these are the parts from the odd-indexed rows of A237270. %C A240020 Also these are the parts in the quadrants 1 and 3 of the spiral described in A239660, see example. %C A240020 Row sums give A008438. %C A240020 The length of row n is A237271(2n-1). %C A240020 Both column 1 and the right border are equal to n. %C A240020 Note that also the sequence can be represented in a quadrant. %C A240020 We can find the spiral (mentioned above) on the terraces of the stepped pyramid described in A244050. - Omar E. Pol, Dec 07 2016 %e A240020 1; %e A240020 2, 2; %e A240020 3, 3; %e A240020 4, 4; %e A240020 5, 3, 5; %e A240020 6, 6; %e A240020 7, 7; %e A240020 8, 8, 8; %e A240020 9, 9; %e A240020 10, 10; %e A240020 11, 5, 5, 11; %e A240020 12, 12; %e A240020 13, 5, 13; %e A240020 14, 6, 6, 14; %e A240020 15, 15; %e A240020 16, 16; %e A240020 17, 7, 7, 17; %e A240020 18, 12, 18; %e A240020 19, 19; %e A240020 20, 8, 8, 20; %e A240020 21, 21; %e A240020 22, 22; %e A240020 23, 32, 23; %e A240020 24, 24; %e A240020 25, 7, 25; %e A240020 ... %e A240020 Illustration of initial terms (rows 1..8): %e A240020 . %e A240020 . _ _ _ _ _ _ _ 7 %e A240020 . |_ _ _ _ _ _ _| %e A240020 . | %e A240020 . |_ _ %e A240020 . _ _ _ _ _ 5 |_ %e A240020 . |_ _ _ _ _| | %e A240020 . |_ _ 3 |_ _ _ 7 %e A240020 . |_ | | | %e A240020 . _ _ _ 3 |_|_ _ 5 | | %e A240020 . |_ _ _| | | | | %e A240020 . |_ _ 3 | | | | %e A240020 . | | | | | | %e A240020 . _ 1 | | | | | | %e A240020 . _ _ _ _ |_| |_| |_| |_| %e A240020 . | | | | | | | | %e A240020 . | | | | | | |_|_ _ %e A240020 . | | | | | | 2 |_ _| %e A240020 . | | | | |_|_ 2 %e A240020 . | | | | 4 |_ %e A240020 . | | |_|_ _ |_ _ _ _ %e A240020 . | | 6 |_ |_ _ _ _| %e A240020 . |_|_ _ _ |_ 4 %e A240020 . 8 | |_ _ | %e A240020 . |_ | |_ _ _ _ _ _ %e A240020 . |_ |_ |_ _ _ _ _ _| %e A240020 . 8 |_ _| 6 %e A240020 . | %e A240020 . |_ _ _ _ _ _ _ _ %e A240020 . |_ _ _ _ _ _ _ _| %e A240020 . 8 %e A240020 . %e A240020 The figure shows the quadrants 1 and 3 of the spiral described in A239660. %e A240020 For n = 5 we have that 2*5 - 1 = 9 and the 9th row of A237593 is [5, 2, 2, 2, 2, 5] and the 8th row of A237593 is [5, 2, 1, 1, 2, 5] therefore between both symmetric Dyck paths there are three regions (or parts) of sizes [5, 3, 5], so row 5 is [5, 3, 5], see the third arm of the spiral in the first quadrant. %e A240020 The sum of divisors of 9 is 1 + 3 + 9 = A000203(9) = 13. On the other hand the sum of the parts of the symmetric representation of sigma(9) is 5 + 3 + 5 = 13, equaling the sum of divisors of 9. %Y A240020 Cf. A000203, A005408, A008438, A112610, A196020, A236104, A237048, A237270, A237271, A237591, A237593, A239053, A239660, A239931, A239933, A244050, A245092, A262626. %K A240020 nonn,tabf %O A240020 1,2 %A A240020 _Omar E. Pol_, Mar 31 2014