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 A239931 #36 Dec 07 2016 11:07:51 %S A239931 1,3,3,5,3,5,7,7,9,9,11,5,5,11,13,5,13,15,15,17,7,7,17,19,19,21,21,23, %T A239931 32,23,25,7,25,27,27,29,11,11,29,31,31,33,9,9,33,35,13,13,35,37,37,39, %U A239931 18,39,41,15,9,15,41,43,11,11,43,45,45,47,17,17,47,49,49,51,51,53,43,43,53,55,55,57,57,59,21,22,21,59,61,11,61,63,15,15,63 %N A239931 Triangle read by rows in which row n lists the parts of the symmetric representation of sigma(4n-3). %C A239931 Row n is a palindromic composition of sigma(4n-3). %C A239931 Row n is also the row 4n-3 of A237270. %C A239931 Row n has length A237271(4n-3). %C A239931 Row sums give A112610. %C A239931 Also row n lists the parts of the symmetric representation of sigma in the n-th arm of the first quadrant of the spiral described in A239660, see example. %C A239931 For the parts of the symmetric representation of sigma(4n-2), see A239932. %C A239931 For the parts of the symmetric representation of sigma(4n-1), see A239933. %C A239931 For the parts of the symmetric representation of sigma(4n), see A239934. %C A239931 We can find the spiral (mentioned above) on the terraces of the pyramid described in A244050. - _Omar E. Pol_, Dec 06 2016 %e A239931 The irregular triangle begins: %e A239931 1; %e A239931 3, 3; %e A239931 5, 3, 5; %e A239931 7, 7; %e A239931 9, 9; %e A239931 11, 5, 5, 11; %e A239931 13, 5, 13; %e A239931 15, 15; %e A239931 17, 7, 7, 17; %e A239931 19, 19; %e A239931 21, 21; %e A239931 23, 32, 23; %e A239931 25, 7, 25; %e A239931 27, 27; %e A239931 29, 11, 11, 29; %e A239931 31, 31; %e A239931 ... %e A239931 Illustration of initial terms in the first quadrant of the spiral described in A239660: %e A239931 . %e A239931 . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 15 %e A239931 . |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| %e A239931 . | %e A239931 . | %e A239931 . _ _ _ _ _ _ _ _ _ _ _ _ _ 13 | %e A239931 . |_ _ _ _ _ _ _ _ _ _ _ _ _| | %e A239931 . | |_ _ _ %e A239931 . | | %e A239931 . _ _ _ _ _ _ _ _ _ _ _ 11 | |_ %e A239931 . |_ _ _ _ _ _ _ _ _ _ _| |_ _ _ |_ %e A239931 . | |_ _ 5 |_ %e A239931 . | |_ |_ |_ _ %e A239931 . _ _ _ _ _ _ _ _ _ 9 |_ _ _ |_ | | %e A239931 . |_ _ _ _ _ _ _ _ _| |_ _ |_ 5 |_|_ | %e A239931 . | |_ _|_ 5 | |_ _ _ _ _ _ 15 %e A239931 . | | |_ | | | %e A239931 . _ _ _ _ _ _ _ 7 |_ _ |_ | |_ _ _ _ _ 13 | | %e A239931 . |_ _ _ _ _ _ _| |_ | | | | | | %e A239931 . | |_ |_|_ _ _ _ 11 | | | | %e A239931 . |_ _ | | | | | | | %e A239931 . _ _ _ _ _ 5 |_ |_ _ _ _ 9 | | | | | | %e A239931 . |_ _ _ _ _| | | | | | | | | | %e A239931 . |_ _ 3 |_ _ _ 7 | | | | | | | | %e A239931 . |_ | | | | | | | | | | | %e A239931 . _ _ _ 3 |_|_ _ 5 | | | | | | | | | | %e A239931 . |_ _ _| | | | | | | | | | | | | %e A239931 . |_ _ 3 | | | | | | | | | | | | %e A239931 . | | | | | | | | | | | | | | %e A239931 . _ 1 | | | | | | | | | | | | | | %e A239931 . |_| |_| |_| |_| |_| |_| |_| |_| %e A239931 . %e A239931 For n = 7 we have that 4*7-3 = 25 and the 25th row of A237593 is [13, 5, 3, 1, 2, 1, 1, 2, 1, 3, 5, 13] and the 24th row of A237593 is [13, 4, 3, 2, 1, 1, 1, 1, 2, 3, 4, 13] therefore between both Dyck paths there are three regions (or parts) of sizes [13, 5, 13], so row 7 is [13, 5, 13]. %e A239931 The sum of divisors of 25 is 1 + 5 + 25 = A000203(25) = 31. On the other hand the sum of the parts of the symmetric representation of sigma(25) is 13 + 5 + 13 = 31, equaling the sum of divisors of 25. %Y A239931 Cf. A000203, A112610, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239660, A239932-A239934, A244050, A245092, A262626. %K A239931 nonn,tabf %O A239931 1,2 %A A239931 _Omar E. Pol_, Mar 29 2014