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A267599 Binary representation of the n-th iteration of the "Rule 177" elementary cellular automaton starting with a single ON (black) cell. 1
1, 1, 1001, 101001, 10101001, 1010101001, 101010101001, 10101010101001, 1010101010101001, 101010101010101001, 10101010101010101001, 1010101010101010101001, 101010101010101010101001, 10101010101010101010101001, 1010101010101010101010101001 (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>2.
G.f.: (1-100*x+1000*x^2) / ((1-x)*(1-100*x)).
(End)
MATHEMATICA
rule=177; 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: A218640 A221347 A109431 * A140927 A261544 A097659
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 18 2016
STATUS
approved

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Last modified April 19 18:05 EDT 2024. Contains 371798 sequences. (Running on oeis4.)