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 A267874 #26 Feb 16 2025 08:33:30
%S A267874 1,2,6,13,22,33,46,61,78,97,118,141,166,193,222,253,286,321,358,397,
%T A267874 438,481,526,573,622,673,726,781,838,897,958,1021,1086,1153,1222,1293,
%U A267874 1366,1441,1518,1597,1678,1761,1846,1933,2022,2113,2206,2301,2398,2497
%N A267874 Total number of ON (black) cells after n iterations of the "Rule 235" elementary cellular automaton starting with a single ON (black) cell.
%C A267874 With the exception of the first one or two entries the same as A123968 and A028872. - _R. J. Mathar_, Jan 24 2016
%H A267874 Robert Price, <a href="/A267874/b267874.txt">Table of n, a(n) for n = 0..1000</a>
%H A267874 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267874 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, 2002; p. 55.
%H A267874 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267874 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A267874 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A267874 From _Colin Barker_, Jan 22 2016 and Apr 20 2019: (Start)
%F A267874 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>2.
%F A267874 G.f.: (1-x+3*x^2-x^4) / (1-x)^3.
%F A267874 (End)
%t A267874 rule=235; 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[Total[Take[nbc,k]],{k,1,rows}] (* Number of Black cells through stage n *)
%Y A267874 Cf. A267869.
%Y A267874 Cf. A028872, A123968.
%K A267874 nonn,easy
%O A267874 0,2
%A A267874 _Robert Price_, Jan 21 2016