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 A267351 Decimal representation of the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell. 2
 1, 5, 14, 119, 56, 2015, 224, 32639, 896, 523775, 3584, 8386559, 14336, 134209535, 57344, 2147450879, 229376, 34359607295, 917504, 549755289599, 3670016, 8796090925055, 14680064, 140737479966719, 58720256, 2251799780130815, 234881024, 36028796884746239 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Robert Price, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. Index entries for sequences related to cellular automata Index to Elementary Cellular Automata FORMULA Conjectures from Colin Barker, Jan 14 2016 and Apr 19 2019: (Start) a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>6. G.f.: (1+5*x-7*x^2+14*x^3-154*x^4-64*x^5+160*x^6) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)). (End) MATHEMATICA rule=123; 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 *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}] (* Decimal Representation of Rows *) CROSSREFS Cf. A267349, A267350. Sequence in context: A316233 A317154 A283785 * A058072 A027304 A070135 Adjacent sequences: A267348 A267349 A267350 * A267352 A267353 A267354 KEYWORD nonn,easy AUTHOR Robert Price, Jan 13 2016 EXTENSIONS Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022 STATUS approved

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Last modified November 30 00:17 EST 2023. Contains 367452 sequences. (Running on oeis4.)