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A267002
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Binary representation of the n-th iteration of the "Rule 83" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 101, 1000, 1101111, 1000000, 11101111111, 1000000000, 111101111111111, 1000000000000, 1111101111111111111, 1000000000000000, 11111101111111111111111, 1000000000000000000, 111111101111111111111111111, 1000000000000000000000, 1111111101111111111111111111111
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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LINKS
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Robert Price, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
Index entries for sequences related to cellular automata
Index to Elementary Cellular Automata
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FORMULA
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Conjectures from Colin Barker, Jan 08 2016 and Apr 19 2019: (Start)
a(n) = 11001*a(n-2)-10011000*a(n-4)+10000000*a(n-6) for n>5.
G.f.: (1+101*x-10001*x^2-9990*x^3+10000*x^4-1100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-1000*x^2)).
(End)
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MATHEMATICA
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rule=83; 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 *)
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CROSSREFS
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Cf. A267001.
Sequence in context: A167842 A244369 A200733 * A242138 A171764 A164842
Adjacent sequences: A266999 A267000 A267001 * A267003 A267004 A267005
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KEYWORD
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nonn
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AUTHOR
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Robert Price, Jan 08 2016
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STATUS
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approved
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