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 A380012 #26 Jun 04 2025 00:30:10 %S A380012 1,4,9,15,21,36,36,57,66,87,81,129,129,162,162,225,228,270,267,351, %T A380012 324,342,483,411,468,516,588,639,600,723,762,777,795,960,888,1071,972, %U A380012 1056,1323,1158,1242,1362,1362,1557,1449,1689,1677,1845,1710,1977,2007,2100,2166,2178,2499,2409,2430,2556 %N A380012 Population of elementary triangular automaton rule 54 at generation n, starting from a lone 1 cell at generation 0. %C A380012 An Elementary Triangular Automaton (ETA) is a cellular automaton in the triangular grid where cells hold binary states and rules are local to the first neighborhood. There are 256 possible ETA rules. %C A380012 Rule 54 (110110 in binary): %C A380012 ----------------------------------------------- %C A380012 |state of the cell |1|1|1|1|0|0|0|0| %C A380012 |sum of the neighbors' states |3|2|1|0|3|2|1|0| %C A380012 |cell's next state |0|0|1|1|0|1|1|0| %C A380012 ----------------------------------------------- %H A380012 Paul Cousin, <a href="/A380012/b380012.txt">Table of n, a(n) for n = 0..16384</a> %H A380012 Paul Cousin, <a href="/A380012/a380012.pdf">Illustration for n = 0..64</a> %H A380012 Paul Cousin, <a href="https://triangular-automata.net">Triangular Automata</a> %H A380012 Paul Cousin, <a href="https://triangular-automata.net/rules.html?rule=54">Rule 54</a> %H A380012 Paul Cousin, <a href="https://triangular-automata.net/?p=integer-sequences">Triangular Automata Integer Sequences</a> %H A380012 Paul Cousin, <a href="https://doi.org/10.25088/ComplexSystems.33.3.253">Triangular Automata: The 256 Elementary Cellular Automata of the Two-Dimensional Plane</a>, Complex Systems, 33(3), 2024, pp. 253-276. %Y A380012 Second center column of ETA rule 54 from a lone 1 cell: A380172. %Y A380012 Third center column of ETA rule 54 from a lone 1 cell: A380173. %K A380012 nonn %O A380012 0,2 %A A380012 _Paul Cousin_, Jan 09 2025