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A267294 Decimal representation of the n-th iteration of the "Rule 121" elementary cellular automaton starting with a single ON (black) cell. 1
1, 1, 26, 59, 476, 751, 7024, 16319, 115136, 195327, 1776384, 4177919, 29474816, 50003967, 454754304, 1069547519, 7545552896, 12801015807, 116417101824, 273804165119, 1931661541376, 3277060046847, 29802778066944, 70093866270719, 494505354592256 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
LINKS
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
Conjectures from Colin Barker, Jan 15 2016 and Apr 19 2019: (Start)
a(n) = a(n-2)+256*a(n-4)-256*a(n-6) for n>12.
G.f.: (1 +x +25*x^2 +58*x^3 +194*x^4 +436*x^5 +148*x^6 +720*x^7 -7088*x^8 +1856*x^9 -15040*x^10 -2816*x^11 +21760*x^12) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1+16*x^2)).
(End)
MATHEMATICA
rule=121; 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. A267292.
Sequence in context: A038861 A277976 A291105 * A162316 A173085 A044128
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 12 2016
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)