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A266435 Binary representation of the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell. 1
1, 111, 0, 1111111, 0, 11111111111, 0, 111111111111111, 0, 1111111111111111111, 0, 11111111111111111111111, 0, 111111111111111111111111111, 0, 1111111111111111111111111111111, 0, 11111111111111111111111111111111111, 0, 111111111111111111111111111111111111111 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Rules 31, 55, 63, 87, 95, 119 and 127 also generate this sequence.

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

LINKS

Robert Price, Table of n, a(n) for n = 0..500

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

FORMULA

Conjectures from Colin Barker, Dec 30 2015 and Apr 15 2019: (Start)

a(n) = ((-1)^n-1)*(1-10^(2*n+1))/18 for n>0.

a(n) = 10001*a(n-2)-10000*a(n-4) for n>4.

G.f.: (1+111*x-10001*x^2+1000*x^3+10000*x^4) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

MATHEMATICA

rule=23; 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. A266434.

Sequence in context: A280141 A280142 A077573 * A216479 A123698 A123727

Adjacent sequences:  A266432 A266433 A266434 * A266436 A266437 A266438

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 29 2015

STATUS

approved

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Last modified July 8 19:20 EDT 2020. Contains 335524 sequences. (Running on oeis4.)