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A267254 Binary representation of the n-th iteration of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell. 1
1, 110, 111, 1111010, 11111, 11111100010, 1011111, 111111111100010, 1011111, 1111111111111100010, 1011111, 11111111111111111100010, 1011111, 111111111111111111111100010, 1011111, 1111111111111111111111111100010, 1011111, 11111111111111111111111111111100010 (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

Index entries for linear recurrences with constant coefficients, signature (0,10001,0,-10000).

FORMULA

From Colin Barker, Jan 13 2016: (Start)

a(n) = 10001*a(n-2)-10000*a(n-4) for n>8.

G.f.: (1 +110*x -9890*x^2 +10900*x^3 -1089000*x^4 +989000*x^5 -109000000*x^6 +110000000*x^7 -10000000000*x^8) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)).

(End)

MATHEMATICA

rule=111; 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) Vec((1 +110*x -9890*x^2 +10900*x^3 -1089000*x^4 +989000*x^5 -109000000*x^6 +110000000*x^7 -10000000000*x^8) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)) + O(x^30)) \\ Colin Barker, Jan 13 2016

CROSSREFS

Cf. A267253.

Sequence in context: A288769 A112891 A182621 * A036230 A171236 A279421

Adjacent sequences:  A267251 A267252 A267253 * A267255 A267256 A267257

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 12 2016

STATUS

approved

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Last modified December 14 21:25 EST 2017. Contains 296020 sequences.