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A266844 Binary representation of the n-th iteration of the "Rule 70" elementary cellular automaton starting with a single ON (black) cell. 1
1, 110, 10100, 1101000, 101010000, 11010100000, 1010101000000, 110101010000000, 10101010100000000, 1101010101000000000, 101010101010000000000, 11010101010100000000000, 1010101010101000000000000, 110101010101010000000000000, 10101010101010100000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Rule 198 also generates 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..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

Index entries for linear recurrences with constant coefficients, signature (10,10000,-100000).

FORMULA

From Colin Barker, Jan 05 2016: (Start)

a(n) = (2^(n-1)*(-9*(-50)^n-2*5^n+209*50^n))/99.

a(n) = 10*a(n-1)+10000*a(n-2)-100000*a(n-3) for n>2.

G.f.: (1+100*x-1000*x^2) / ((1-10*x)*(1-100*x)*(1+100*x)).

(End)

MATHEMATICA

rule=70; 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 *)

PROG

(PARI) a(n) = (2^(n-1)*(-9*(-50)^n-2*5^n+209*50^n))/99 \\ Colin Barker, Jan 05 2016

(PARI) Vec((1+100*x-1000*x^2)/((1-10*x)*(1-100*x)*(1+100*x)) + O(x^20)) \\ Colin Barker, Jan 05 2016

CROSSREFS

Cf. A266843.

Sequence in context: A063751 A266179 A163664 * A265319 A267854 A135645

Adjacent sequences:  A266841 A266842 A266843 * A266845 A266846 A266847

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 04 2016

STATUS

approved

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Last modified March 26 16:33 EDT 2019. Contains 321510 sequences. (Running on oeis4.)