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A267350 Binary representation of the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell. 1
1, 101, 1110, 1110111, 111000, 11111011111, 11100000, 111111101111111, 1110000000, 1111111110111111111, 111000000000, 11111111111011111111111, 11100000000000, 111111111111101111111111111, 1110000000000000, 1111111111111110111111111111111, 111000000000000000 (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

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

FORMULA

Conjectures from Colin Barker, Jan 14 2016: (Start)

a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>6.

G.f.: (1+101*x-8991*x^2+89910*x^3-10091010*x^4-200000*x^5+10100000*x^6) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).

(End)

MATHEMATICA

rule=123; 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. A267349.

Sequence in context: A280340 A283589 A284403 * A290526 A290827 A290835

Adjacent sequences:  A267347 A267348 A267349 * A267351 A267352 A267353

KEYWORD

nonn

AUTHOR

Robert Price, Jan 13 2016

STATUS

approved

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Last modified July 23 22:38 EDT 2019. Contains 325278 sequences. (Running on oeis4.)