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 A266299 Binary representation of the n-th iteration of the "Rule 14" elementary cellular automaton starting with a single ON (black) cell. 3
 1, 110, 11000, 1100000, 110000000, 11000000000, 1100000000000, 110000000000000, 11000000000000000, 1100000000000000000, 110000000000000000000, 11000000000000000000000, 1100000000000000000000000, 110000000000000000000000000, 11000000000000000000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Rules 46, 142 and 174 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 linear recurrences with constant coefficients, signature (100). FORMULA From Colin Barker, Dec 28 2015: (Start) a(n) = 11*10^(2*n-1) for n>0. a(n) = 100*a(n-1) for n>1. G.f.: (1+10*x) / (1-100*x). (End) MATHEMATICA rule=14; 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 (PARI) Vec((1+10*x)/(1-100*x) + O(x^100)) \\ Colin Barker, Dec 28 2015 CROSSREFS Cf. A266298. Sequence in context: A265319 A267854 A135645 * A265696 A267535 A267577 Adjacent sequences:  A266296 A266297 A266298 * A266300 A266301 A266302 KEYWORD nonn,easy AUTHOR Robert Price, Dec 26 2015 STATUS approved

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Last modified March 24 11:34 EDT 2019. Contains 321448 sequences. (Running on oeis4.)