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A267613 Binary representation of the n-th iteration of the "Rule 185" elementary cellular automaton starting with a single ON (black) cell. 2
1, 1, 1011, 101111, 10111111, 1011111111, 101111111111, 10111111111111, 1011111111111111, 101111111111111111, 10111111111111111111, 1011111111111111111111, 101111111111111111111111, 10111111111111111111111111, 1011111111111111111111111111 (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 18 2016 and Apr 20 2019: (Start)
a(n) = 101*a(n-1) - 100*a(n-2) for n>3.
G.f.: (1-100*x+1010*x^2-900*x^3) / ((1-x)*(1-100*x)).
(End)
MATHEMATICA
rule=185; 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 *)
CROSSREFS
Sequence in context: A183849 A185881 A115769 * A178396 A178349 A291962
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 18 2016
STATUS
approved

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Last modified February 27 10:59 EST 2024. Contains 370378 sequences. (Running on oeis4.)