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 A279388 #49 Jun 13 2021 03:25:21 %S A279388 1,3,4,7,6,11,1,8,15,13,18,12,23,5,14,24,23,1,31,18,35,4,20,39,3,32, %T A279388 36,24,47,13,31,42,40,55,1,30,59,13,32,63,48,54,45,3,71,20,38,60,56, %U A279388 79,11,42,83,13,44,84,73,5,72,48,95,29,57,93,72,98,54,107,13,72,111,9,80,90,60,119,37,12 %N A279388 Irregular triangle read by rows: T(n,k) is the sum of the subparts in the k-th layer of the symmetric representation of sigma(n), if such a layer exists. %H A279388 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a> %e A279388 Triangle begins (first 15 rows): %e A279388 1; %e A279388 3; %e A279388 4; %e A279388 7; %e A279388 6; %e A279388 11, 1; %e A279388 8; %e A279388 15; %e A279388 13; %e A279388 18; %e A279388 12; %e A279388 23, 5; %e A279388 14; %e A279388 24; %e A279388 23, 1; %e A279388 ... %e A279388 For n = 12 we have that the 11th row of triangle A237593 is [6, 3, 1, 1, 1, 1, 3, 6] and the 12th row of the same triangle is [7, 2, 2, 1, 1, 2, 2, 7], so the diagram of the symmetric representation of sigma(12) = 28 is constructed as shown below in Figure 1: %e A279388 . _ _ %e A279388 . | | | | %e A279388 . | | | | %e A279388 . | | | | %e A279388 . | | | | %e A279388 . | | | | %e A279388 . _ _ _| | _ _ _| | %e A279388 . 28 _| _ _| 23 _| _ _ _| %e A279388 . _| | _| _| | %e A279388 . | _| | _| _| %e A279388 . | _ _| | |_ _| %e A279388 . _ _ _ _ _ _| | _ _ _ _ _ _| | 5 %e A279388 . |_ _ _ _ _ _ _| |_ _ _ _ _ _ _| %e A279388 . %e A279388 . Figure 1. The symmetric Figure 2. After the dissection %e A279388 . representation of sigma(12) of the symmetric representation %e A279388 . has only one part which of sigma(12) into layers of %e A279388 . contains 28 cells, so width 1 we can see two "subparts" %e A279388 . A000203(12) = 28. that contain 23 and 5 cells %e A279388 . respectively, so the 12th row of %e A279388 . this triangle is [23, 5]. %e A279388 . %e A279388 For n = 15 we have that the 14th row of triangle A237593 is [8, 3, 1, 2, 2, 1, 3, 8] and the 15th row of the same triangle is [8, 3, 2, 1, 1, 1, 1, 2, 3, 8], so the diagram of the symmetric representation of sigma(15) is constructed as shown below in Figure 3: %e A279388 . _ _ %e A279388 . | | | | %e A279388 . | | | | %e A279388 . | | | | %e A279388 . | | | | %e A279388 . 8 | | 8 | | %e A279388 . | | | | %e A279388 . | | | | %e A279388 . _ _ _|_| _ _ _|_| %e A279388 . 8 _ _| | 7 _ _| | %e A279388 . | _| | _ _| %e A279388 . _| _| _| |_| %e A279388 . |_ _| |_ _| 1 %e A279388 . 8 | 8 | %e A279388 . _ _ _ _ _ _ _ _| _ _ _ _ _ _ _ _| %e A279388 . |_ _ _ _ _ _ _ _| |_ _ _ _ _ _ _ _| %e A279388 . %e A279388 . Figure 3. The symmetric Figure 4. After the dissection %e A279388 . representation of sigma(15) of the symmetric representation %e A279388 . has three parts of size 8, of sigma(15) into layers of %e A279388 . whose sum is 8 + 8 + 8 = 24, width 1 we can see four "subparts". %e A279388 . so A000203(15) = 24. The first layer has three subparts %e A279388 . whose sum is 8 + 7 + 8 = 23. The %e A279388 . second layer has only one subpart %e A279388 . of size 1, so the 15th row of this %e A279388 . triangle is [23, 1]. %e A279388 . %Y A279388 For the definition of "subparts" see A279387. %Y A279388 For the triangle of subparts see A279391. %Y A279388 Row sums give A000203. %Y A279388 Row n has length A250068(n). %Y A279388 Cf. A001227, A005279, A196020, A235791, A236104, A237048, A237270, A237591, A237593, A239657, A244050, A245092, A250070, A261699, A262626. %K A279388 nonn,tabf %O A279388 1,2 %A A279388 _Omar E. Pol_, Dec 12 2016