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 A261692 #44 Apr 02 2017 17:17:42 %S A261692 0,1,4,5,12,17,20,21,36,49,60,69,76,81,84,85,116,145,172,197,220,241, %T A261692 260,277,292,305,316,325,332,337,340,341,404,465,524,581,636,689,740, %U A261692 789,836,881,924,965,1004,1041,1076,1109,1140,1169,1196,1221,1244,1265,1284,1301,1316,1329,1340,1349,1356,1361,1364,1365,1492 %N A261692 Number of "ON" cells after n-th stage in a cellular automaton in a 90-degree wedge on the square grid. (See Comments lines for definition.) %C A261692 In order to construct the structure we use the following rules: %C A261692 - On the square grid we are in a 90-degree wedge with the vertex located on top of the wedge. %C A261692 - At stage 0 there are no ON cells, so a(0) = 0. %C A261692 - At stage 1 we turn ON the nearest cell of the vertex, so a(1) = 1. %C A261692 - The cells turned ON remain ON forever. %C A261692 - 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 structure. %C A261692 - 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 structure, where k is the number of ON cells in row n - 1. %C A261692 - The "ON" cells of row n must be centered respect to the "ON" cells of row n - 1. %C A261692 Note that the structure seems to grow into the holes of a virtual structure similar to the Sierpiński's triangle but using square cells (see example). %C A261692 A261693 gives the number of cells turned "ON" at n-th stage. %C A261692 This is analog of A255748, but here we are working on the square grid. %H A261692 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 A261692 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a> %F A261692 a(n) = (A262620(n) - 1)/4. %e A261692 Illustration of initial terms (n = 0..15): %e A261692 ------------------------------------------------------ %e A261692 n A261692(n) a(n) Diagram %e A261692 ------------------------------------------------------ %e A261692 0 0 0 /_\ %e A261692 1 1 1 /_|_|_\ %e A261692 2 3 4 / |_|_|_| \ %e A261692 3 1 5 /_ _ _|_|_ _ _\ %e A261692 4 7 12 / |_|_|_|_|_|_|_| \ %e A261692 5 5 17 / |_|_|_|_|_| \ %e A261692 6 3 20 / |_|_|_| \ %e A261692 7 1 21 /_ _ _ _ _ _ _|_|_ _ _ _ _ _ _\ %e A261692 8 15 36 / |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| \ %e A261692 9 13 49 |_|_|_|_|_|_|_|_|_|_|_|_|_| %e A261692 10 11 60 |_|_|_|_|_|_|_|_|_|_|_| %e A261692 11 9 69 |_|_|_|_|_|_|_|_|_| %e A261692 12 7 76 |_|_|_|_|_|_|_| %e A261692 13 5 81 |_|_|_|_|_| %e A261692 14 3 84 |_|_|_| %e A261692 15 1 85 |_| %e A261692 ... %e A261692 After 15 generations there are 85 ON cells in the structure, so a(15) = 85. %Y A261692 Cf. A001316, A047999, A139250, A147562, A255748, A261693, A262620. %K A261692 nonn,look %O A261692 0,3 %A A261692 _Omar E. Pol_, Sep 25 2015