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 A262620 #28 Apr 02 2017 17:16:39 %S A262620 1,5,17,21,49,69,81,85,145,197,241,277,305,325,337,341,465,581,689, %T A262620 789,881,965,1041,1109,1169,1221,1265,1301,1329,1349,1361,1365,1617, %U A262620 1861,2097,2325,2545,2757,2961,3157,3345,3525,3697,3861,4017,4165,4305,4437,4561,4677,4785,4885,4977,5061,5137,5205,5265,5317,5361,5397 %N A262620 Number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton on the square grid (see Comments lines for definition). %C A262620 On the infinite square grid consider four 90-degree wedges forming a "X" with the vertex located at the center of a cell. %C A262620 At stage 0 we start with an ON cell in the vertex of the wedges, so a(0) = 1. %C A262620 In order to construct the structure we use the following rules for the South wedge: %C A262620 - The cells turned ON remain ON forever. %C A262620 - At stage 1 we turn ON the nearest cell to the initial ON cell. %C A262620 - If n is a power of 2, at stage n we turn "ON" 2*n - 1 connected cells in the n-th row of the wedge. %C A262620 - Otherwise, if n is not a power of 2, at stage n we turn "ON" k - 2 connected cells in the n-th row of the wedge, where k is the number of ON cells in row n - 1. %C A262620 - The "ON" cells of row n must be centered respect to the "ON" cells of row n - 1. %C A262620 The structures in the other three wedges are copies of the structure in the South wedge but they grow in direction East, North and West. %C A262620 Note that in every wedge the structure seems to grow into the holes of a virtual structure similar to the Sierpiński's triangle but using square cells. %C A262620 A262621 gives the number of cells turned "ON" at n-th stage. %C A262620 This is analog of A256266, but here we are working on the square grid and we have four wedges, not six wedges. %H A262620 N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a> %H A262620 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a> %F A262620 a(n) = 1 + 4*A261692(n). %e A262620 Illustration of the structure after 15 generations: %e A262620 . %e A262620 . O %e A262620 . O O O %e A262620 . O O O O O %e A262620 . O O O O O O O %e A262620 . O O O O O O O O O %e A262620 . O O O O O O O O O O O %e A262620 . O O O O O O O O O O O O O %e A262620 . O O O O O O O O O O O O O O O %e A262620 . O O O %e A262620 . O O O O O O O %e A262620 . O O O O O O O O O O O %e A262620 . O O O O O O O O O O O O O O O %e A262620 . O O O O O O O O O O O O O %e A262620 . O O O O O O O O O O O O O O O O O O O %e A262620 . O O O O O O O O O O O O O O O O O O O O O O O %e A262620 . O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O %e A262620 . O O O O O O O O O O O O O O O O O O O O O O O %e A262620 . O O O O O O O O O O O O O O O O O O O %e A262620 . O O O O O O O O O O O O O %e A262620 . O O O O O O O O O O O O O O O %e A262620 . O O O O O O O O O O O %e A262620 . O O O O O O O %e A262620 . O O O %e A262620 . O O O O O O O O O O O O O O O %e A262620 . O O O O O O O O O O O O O %e A262620 . O O O O O O O O O O O %e A262620 . O O O O O O O O O %e A262620 . O O O O O O O %e A262620 . O O O O O %e A262620 . O O O %e A262620 . O %e A262620 . %e A262620 There are 341 ON cells in the structure, so a(15) = 341. %e A262620 Note that every circle in the structure should be replaced with a square cell. %Y A262620 Cf. A147562, A160720, A256266, A261692, A261693, A262621. %K A262620 nonn,look %O A262620 0,2 %A A262620 _Omar E. Pol_, Oct 16 2015