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 A385414 #15 Jul 23 2025 16:14:05 %S A385414 2,2,3,24,70,584,1325,2082,5304,6327,10679,11822 %N A385414 Number of distinct states of Conway's Game of Life, starting from an n-th level Hilbert curve on a toroidal 2^(n+1)-1 by 2^(n+1)-1 grid. %C A385414 The curve is taken with segments of length 2 so that it follows a path through coordinates (2*A059252(t), 2*A059253(t)) for 0 <= t < 2^n. %C A385414 The size of the toroidal grid is the extent of these coordinates so that the cells on one edge are immediately adjacent to the cells on the opposite side. %C A385414 The grid has a fixed position and orientation and states differing at any cell are distinct. %e A385414 For n=0, the curve is a single cell on a 1 X 1 toroidal grid and has a(0) = 2 states: initially live, then dead and remaining so. %e A385414 For n=2 the initial state and two subsequent states are %e A385414 o o o . o o o | . . . . . . . | . . . . . . . | %e A385414 o . o . o . o | . . . . . . . | . . . . . . . | %e A385414 o . o o o . o | . . o . o . . | . . . . . . . | %e A385414 o . . . . . o | . . . . . . . | . . . . . . . | %e A385414 o o o . o o o | . . o . o . . | . . . . . . . | %e A385414 . . o . o . . | . . . . . . . | . . . . . . . | %e A385414 o o o . o o o | . . . . . . . | . . . . . . . | %e A385414 (generation 1) (generation 2) (generation 3) %e A385414 Every generation after 3 is identical to generation 3, so this sequence has 3 distinct states. Thus, a(2) = 3. %Y A385414 Cf. A059252, A059253. %K A385414 nonn,more %O A385414 0,1 %A A385414 _Luke Bennet_, Jun 27 2025