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A267854 Binary representation of the n-th iteration of the "Rule 230" elementary cellular automaton starting with a single ON (black) cell. 1
1, 110, 10100, 1111000, 101110000, 11101100000, 1011101000000, 111011110000000, 10111011100000000, 1110111011000000000, 101110111010000000000, 11101110111100000000000, 1011101110111000000000000, 111011101110110000000000000, 10111011101110100000000000000 (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 (0,10000,0,10000,0,-100000000).

FORMULA

From Colin Barker, Jan 21 2016: (Start)

a(n) = 10000*a(n-2)+10000*a(n-4)-100000000*a(n-6) for n>5.

G.f.: (1+110*x+100*x^2+11000*x^3+100000*x^4-10000000*x^5) / ((1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)*(1+100*x^2)).

(End)

MATHEMATICA

rule=230; 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+100*x^2+11000*x^3+100000*x^4-10000000*x^5)/((1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)*(1+100*x^2)) + O(x^20)) \\ Colin Barker, Jan 21 2016

CROSSREFS

Cf. A267853.

Sequence in context: A163664 A266844 A265319 * A135645 A266299 A265696

Adjacent sequences:  A267851 A267852 A267853 * A267855 A267856 A267857

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 21 2016

STATUS

approved

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Last modified March 21 07:23 EDT 2019. Contains 321367 sequences. (Running on oeis4.)