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A267815 Binary representation of the n-th iteration of the "Rule 221" elementary cellular automaton starting with a single ON (black) cell. 1
1, 11, 10111, 1101111, 111011111, 11110111111, 1111101111111, 111111011111111, 11111110111111111, 1111111101111111111, 111111111011111111111, 11111111110111111111111, 1111111111101111111111111, 111111111111011111111111111, 11111111111110111111111111111 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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 22 2016 and Apr 20 2019: (Start)
a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3) for n>3.
G.f.: (1-100*x+10000*x^2-10000*x^3) / ((1-x)*(1-10*x)*(1-100*x)).
(End)
MATHEMATICA
rule=221; 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
Cf. A267814.
Sequence in context: A161761 A114754 A157709 * A121520 A308335 A083442
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 20 2016
STATUS
approved

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Last modified May 24 11:59 EDT 2024. Contains 372773 sequences. (Running on oeis4.)