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 A267884 Total number of OFF (white) cells after n iterations of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell. 1
 0, 3, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. LINKS Robert Price, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton S. Wolfram, A New Kind of Science Index entries for linear recurrences with constant coefficients, signature (1). FORMULA From Colin Barker, Jan 24 2016: (Start) a(n) = 6 for n>2. a(n) = a(n-1) for n>3. G.f.: x*(3+2*x+x^2) / (1-x). (End) MATHEMATICA rule=233; 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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc, k]], {k, 1, rows}] (* Number of White cells through stage n *) PROG (PARI) concat(0, Vec(x*(3+2*x+x^2)/(1-x) + O(x^100))) \\ Colin Barker, Jan 24 2016 CROSSREFS Cf. A267868. Sequence in context: A161435 A224831 A281591 * A077859 A123572 A244953 Adjacent sequences:  A267881 A267882 A267883 * A267885 A267886 A267887 KEYWORD nonn,easy AUTHOR Robert Price, Jan 21 2016 STATUS approved

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Last modified February 16 18:53 EST 2019. Contains 320165 sequences. (Running on oeis4.)