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 A266753 Decimal representation of the n-th iteration of the "Rule 163" elementary cellular automaton starting with a single ON (black) cell. 3
 1, 4, 18, 74, 298, 1194, 4778, 19114, 76458, 305834, 1223338, 4893354, 19573418, 78293674, 313174698, 1252698794, 5010795178, 20043180714, 80172722858, 320690891434, 1282763565738, 5131054262954, 20524217051818, 82096868207274, 328387472829098 (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 sequences related to cellular automata Index to Elementary Cellular Automata FORMULA Conjectures from Colin Barker, Jan 20 2016 and Apr 20 2019: (Start) a(n) = 5*a(n-1)-4*a(n-2) for n>2. G.f.: (1-x+2*x^2) / ((1-x)*(1-4*x)). (End) Empirical a(n) = (7*4^n - 4)/6 for n>1. - Colin Barker, Nov 25 2016 and Apr 20 2019 a(n) = 4*a(n-1) + 2, n>1, conjectured. - Yosu Yurramendi, Jan 22 2017 a(n) = 2*A020988(n) - A020988(n-1) = A020988(n) + 2^(2n-1) for n > 0, conjectured. - Yosu Yurramendi, Jan 24 2017 [n range correction - Karl V. Keller, Jr., May 07 2022] a(n) = A072197(n-1) + A002450(n), n > 0, conjectured. - Yosu Yurramendi, Mar 03 2017 MATHEMATICA rule=163; 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. A263919, A266752. Sequence in context: A202358 A075675 A047034 * A307323 A218059 A069008 Adjacent sequences: A266750 A266751 A266752 * A266754 A266755 A266756 KEYWORD nonn,easy AUTHOR Robert Price, Jan 17 2016 EXTENSIONS Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - N. J. A. Sloane, Jun 13 2022 STATUS approved

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Last modified September 8 22:43 EDT 2024. Contains 375759 sequences. (Running on oeis4.)