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 A266222 #17 Feb 16 2025 08:33:28
%S A266222 0,1,5,0,9,0,13,0,17,0,21,0,25,0,29,0,33,0,37,0,41,0,45,0,49,0,53,0,
%T A266222 57,0,61,0,65,0,69,0,73,0,77,0,81,0,85,0,89,0,93,0,97,0,101,0,105,0,
%U A266222 109,0,113,0,117,0,121,0,125,0,129,0,133,0,137,0,141,0
%N A266222 Number of OFF (white) cells in the n-th iteration of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.
%D A266222 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266222 Robert Price, <a href="/A266222/b266222.txt">Table of n, a(n) for n = 0..499</a>
%H A266222 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266222 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266222 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A266222 Conjectures from _Colin Barker_, Dec 26 2015 and Apr 13 2019: (Start)
%F A266222 a(n) = 1/2*(1+(-1)^n)*(1+2*n) for n>1.
%F A266222 a(n) = 2*a(n-2) - a(n-4) for n>5.
%F A266222 G.f.: x*(1+5*x-2*x^2-x^3+x^4) / ((1-x)^2*(1+x)^2).
%F A266222 (End)
%t A266222 rule=7; rows=20; ca=CellularAutomaton[rule,{{1},0},rows-1,{All,All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]],{rows-k+1,rows+k-1}],{k,1,rows}]; (* Truncated list of each row *) nbc=Table[Total[catri[[k]]],{k,1,rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}] (* Number of White cells in stage n *)
%Y A266222 Cf. A266216.
%K A266222 nonn,easy
%O A266222 0,3
%A A266222 _Robert Price_, Dec 24 2015