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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

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

Index entries for linear recurrences with constant coefficients, signature (101,-100).

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

Cf. A267612, A267614.

Sequence in context: A183849 A185881 A115769 * A178396 A178349 A291962

Adjacent sequences:  A267610 A267611 A267612 * A267614 A267615 A267616

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 18 2016

STATUS

approved

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Last modified August 10 13:12 EDT 2022. Contains 356039 sequences. (Running on oeis4.)