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A267359 Binary representation of the n-th iteration of the "Rule 125" elementary cellular automaton starting with a single ON (black) cell. 1
1, 11, 11100, 101111, 111110000, 1000111111, 1111101000000, 10001111111111, 11111010000000000, 100011111111111111, 111110100000000000000, 1000111111111111111111, 1111101000000000000000000, 10001111111111111111111111, 11111010000000000000000000000 (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 14 2016: (Start)

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

G.f.: (1 +11*x +1099*x^2 -8900*x^3 +108900*x^4 -10990000*x^5 +890000*x^6 +11000000*x^7 -1000000*x^8) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)).

(End)

MATHEMATICA

rule=125; 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 +11*x +1099*x^2 -8900*x^3 +108900*x^4 -10990000*x^5 +890000*x^6 +11000000*x^7 -1000000*x^8)/((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)) + O(x^20)) \\ Colin Barker, Jan 14 2016

CROSSREFS

Cf. A267358.

Sequence in context: A068223 A068224 A066945 * A267940 A113615 A034873

Adjacent sequences:  A267356 A267357 A267358 * A267360 A267361 A267362

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 13 2016

STATUS

approved

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Last modified December 15 01:20 EST 2018. Contains 318141 sequences. (Running on oeis4.)