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A267351 Decimal representation of the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell. 1
1, 5, 14, 119, 56, 2015, 224, 32639, 896, 523775, 3584, 8386559, 14336, 134209535, 57344, 2147450879, 229376, 34359607295, 917504, 549755289599, 3670016, 8796090925055, 14680064, 140737479966719, 58720256, 2251799780130815, 234881024, 36028796884746239 (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 and Apr 19 2019: (Start)

a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>6.

G.f.: (1+5*x-7*x^2+14*x^3-154*x^4-64*x^5+160*x^6) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*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]], 2], {k, 1, rows}]   (* Decimal Representation of Rows *)

CROSSREFS

Cf. A267349.

Sequence in context: A316233 A317154 A283785 * A058072 A027304 A070135

Adjacent sequences:  A267348 A267349 A267350 * A267352 A267353 A267354

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 13 2016

STATUS

approved

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Last modified May 16 18:13 EDT 2021. Contains 343949 sequences. (Running on oeis4.)