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A266668 Decimal representation of the n-th iteration of the "Rule 51" elementary cellular automaton starting with a single ON (black) cell. 1
1, 5, 4, 119, 16, 2015, 64, 32639, 256, 523775, 1024, 8386559, 4096, 134209535, 16384, 2147450879, 65536, 34359607295, 262144, 549755289599, 1048576, 8796090925055, 4194304, 140737479966719, 16777216, 2251799780130815, 67108864, 36028796884746239, 268435456 (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 03 2016 and Apr 18 2019: (Start)

a(n) = (-1/2-(-4)^n+(-2)^n+(-1)^n/2+4^n).

G.f.: (1+7*x-3*x^2+8*x^3+32*x^4) / ((1-x)*(1+x)*(1+2*x)*(1-4*x)*(1+4*x)).

(End)

MATHEMATICA

rule=51; 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. A266666.

Sequence in context: A264880 A128191 A186639 * A043299 A144776 A065937

Adjacent sequences:  A266665 A266666 A266667 * A266669 A266670 A266671

KEYWORD

nonn

AUTHOR

Robert Price, Jan 02 2016

STATUS

approved

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Last modified March 28 11:00 EDT 2020. Contains 333083 sequences. (Running on oeis4.)