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 A266180 Decimal representation of the n-th iteration of the "Rule 6" elementary cellular automaton starting with a single ON (black) cell. 6
 1, 6, 16, 96, 256, 1536, 4096, 24576, 65536, 393216, 1048576, 6291456, 16777216, 100663296, 268435456, 1610612736, 4294967296, 25769803776, 68719476736, 412316860416, 1099511627776, 6597069766656, 17592186044416, 105553116266496, 281474976710656 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A001025 is a subsequence. - Altug Alkan, Dec 23 2015 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 Hans Montanus and Ron Westdijk, Cellular Automation and Binomials, Math around the Block (2022), p. 22. Eric Weisstein's World of Mathematics, Elementary Cellular Automaton Index entries for sequences related to cellular automata Index to Elementary Cellular Automata Index entries for linear recurrences with constant coefficients, signature (0,16). FORMULA From Colin Barker, Dec 23 2015 and Apr 13 2019: (Start) a(n) = 4^(n-1)*(5-(-1)^n). a(n) = 16*a(n-2) for n>1. G.f.: (1+6*x) / ((1-4*x)*(1+4*x)). (End) 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]], 2], {k, 1, rows}] (* Decimal Representation of Rows *) LinearRecurrence[{0, 16}, {1, 6}, 30] (* Harvey P. Dale, May 25 2016 *) PROG (Python) print([int(4**(n-1)*(5-(-1)**n)) for n in range(30)]) # Karl V. Keller, Jr., Jun 03 2021 CROSSREFS Cf. A001025, A266178, A266179, A019590, A003953, A003945, A000034, A032766, A042948, A035608. Sequence in context: A056204 A091148 A210370 * A229566 A222965 A009354 Adjacent sequences: A266177 A266178 A266179 * A266181 A266182 A266183 KEYWORD nonn,easy AUTHOR Robert Price, Dec 22 2015 STATUS approved

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Last modified May 29 11:46 EDT 2023. Contains 363042 sequences. (Running on oeis4.)