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A267937 Binary representation of the n-th iteration of the "Rule 251" elementary cellular automaton starting with a single ON (black) cell. 2
1, 101, 11111, 1111111, 111111111, 11111111111, 1111111111111, 111111111111111, 11111111111111111, 1111111111111111111, 111111111111111111111, 11111111111111111111111, 1111111111111111111111111, 111111111111111111111111111, 11111111111111111111111111111 (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 23 2016 and Apr 16 2019: (Start)

a(n) = 101*a(n-1)-100*a(n-2) for n>3.

G.f.: (1+1010*x^2-1000*x^3) / ((1-x)*(1-100*x)).

(End)

MATHEMATICA

rule=251; 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. A267936.

Sequence in context: A267920 A300570 A171825 * A068160 A185893 A156669

Adjacent sequences:  A267934 A267935 A267936 * A267938 A267939 A267940

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 22 2016

STATUS

approved

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Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)