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 A211999 #38 Jul 18 2022 22:47:21 %S A211999 1,1,1,2,2,1,1,1,1,3,3,1,1,1,1,1,2,1,1,2,2,4,4,1,2,2,1,2,1,1,1,1,1,1, %T A211999 1,1,3,1,1,3,2,5,5,1,3,2,1,3,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,4,1, %U A211999 1,2,2,2,4,2,3,3,6,6,1,3,3,1,4,2,1,2,2,2,1,4,1,1,1,2,2,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,3,2,1,1,5,1,1,3,2,2,5,2,4,3,7 %N A211999 A list of ordered partitions of the positive integers in which the shells of each integer are assembled by their tails. %C A211999 The sequence lists the partitions of all positive integers. Each row of the irregular array is a partition of j. %C A211999 At stage 1, we start with 1. %C A211999 At stage j > 1, we write the partitions of j using the following rules: %C A211999 First we copy the last A000041(j-1) rows of the array in descending order, as a mirror image, starting with the row that contains the part of size j-1. At the end of each new row, we added a part of size 1. %C A211999 Second, we write the partitions of j that do not contain 1 as a part, in reverse-lexicographic order, such that the last row (or partition of j) is j. %C A211999 Note that the table can be partially folded. In this case we have a three-dimensional structure in which each column contains parts of the same size (see example). Also the table can be completely folded, therefore stacked parts have the same size. %H A211999 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpa401.jpg">Illustration of initial terms</a> %e A211999 A table of partitions. %e A211999 --------------------------------------------------------- %e A211999 . Expanded Geometric Side view of the %e A211999 Partitions version model folded table %e A211999 --------------------------------------------------------- %e A211999 1; 1; |*| / %e A211999 --------------------------------------------------------- %e A211999 1,1; 1,1; |o|*| \ %e A211999 2; . 2; |* *| \ %e A211999 --------------------------------------------------------- %e A211999 2,1; . 2,1; |o o|*| / %e A211999 1,1,1; 1,1,1; |o|o|*| / %e A211999 3; . . 3; |* * *| / %e A211999 --------------------------------------------------------- %e A211999 3,1; . . 3,1; |o o o|*| \ %e A211999 1,1,1,1; 1,1,1,1; |o|o|o|*| \ %e A211999 2,1,1; . 2,1,1; |o o|o|*| \ %e A211999 2,2; . 2,. 2; |* *|* *| \ %e A211999 4; . . . 4; |* * * *| \ %e A211999 --------------------------------------------------------- %e A211999 4,1; . . . 4,1; |o o o o|*| / %e A211999 2,2,1; . 2,. 2,1; |o o|o o|*| / %e A211999 2,1,1,1; . 2,1,1,1; |o o|o|o|*| / %e A211999 1,1,1,1,1; 1,1,1,1,1; |o|o|o|o|*| / %e A211999 3,1,1; . . 3,1,1; |o o o|o|*| / %e A211999 3,2; . . 3,. 2; |* * *|* *| / %e A211999 5; . . . . 5; |* * * * *| / %e A211999 --------------------------------------------------------- %e A211999 5,1; . . . . 5,1; |o o o o o|*| \ %e A211999 3,2,1; . . 3,. 2,1; |o o o|o o|*| \ %e A211999 3,1,1,1; . . 3,1,1,1; |o o o|o|o|*| \ %e A211999 1,1,1,1,1,1; 1,1,1,1,1,1; |o|o|o|o|o|*| \ %e A211999 2,1,1,1,1; . 2,1,1,1,1; |o o|o|o|o|*| \ %e A211999 2,2,1,1; . 2,. 2,1,1; |o o|o o|o|*| \ %e A211999 4,1,1; . . . 4,1,1; |o o o o|o|*| \ %e A211999 2,2,2; . 2, .2,. 2; |* *|* *|* *| \ %e A211999 4,2; . . . 4,. 2; |* * * *|* *| \ %e A211999 3,3; . . 3,. . 3; |* * *|* * *| \ %e A211999 6; . . . . . 6; |* * * * * *| \ %e A211999 --------------------------------------------------------- %e A211999 Note that * is a unitary element of every part of the last section of j. %Y A211999 Rows sums give A036042, n>=1. %Y A211999 Other versions are A211983, A211984, A211989. See also A026792, A211992-A211994. Spiral arrangements are A211985-A211988, A211995-A211998. %Y A211999 Cf. A000041, A026905, A135010, A138121, A138137, A138879, A182703, A206437. %K A211999 nonn,tabf %O A211999 1,4 %A A211999 _Omar E. Pol_, Aug 14 2012