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 A266179 Binary representation of the n-th iteration of the "Rule 6" elementary cellular automaton starting with a single ON (black) cell. 6
 1, 110, 10000, 1100000, 100000000, 11000000000, 1000000000000, 110000000000000, 10000000000000000, 1100000000000000000, 100000000000000000000, 11000000000000000000000, 1000000000000000000000000, 110000000000000000000000000, 10000000000000000000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Rules 38,134 and 166 also generate this sequence. REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. LINKS Robert Price, Table of n, a(n) for n = 0..999 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 From Colin Barker, Dec 23 2015 and Apr 13 2019: (Start) a(n) = 4^(n-1)*5^(2*n-1)*(21-(-1)^n). a(n) = 10000*a(n-2) for n>1. G.f.: (1+110*x) / ((1-100*x)*(1+100*x)). (End) a(n) = 110*100^(n-1) for odd n; a(n) = 100^n for even n. - Karl V. Keller, Jr., Aug 11 2021 MATHEMATICA rule=6; 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]]], {k, 1, rows}] (* Binary Representation of Rows *) PROG (Python) print([110*100**(n-1) if n%2 else 100**n for n in range(30)]) # Karl V. Keller, Jr., Aug 11 2021 CROSSREFS Cf. A266178, A266180. Sequence in context: A111784 A146495 A063751 * A163664 A266844 A265319 Adjacent sequences: A266176 A266177 A266178 * A266180 A266181 A266182 KEYWORD nonn,easy AUTHOR Robert Price, Dec 22 2015 STATUS approved

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Last modified June 10 09:57 EDT 2023. Contains 363199 sequences. (Running on oeis4.)