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A267138 Binary representation of the n-th iteration of the "Rule 103" elementary cellular automaton starting with a single ON (black) cell. 1
1, 110, 110, 1110101, 111100, 11110001011, 101111000, 111111100010111, 1011110000, 1111111111000101111, 10111100000, 11111111111110001011111, 101111000000, 111111111111111100010111111, 1011110000000, 1111111111111111111000101111111, 10111100000000 (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 (0,10011,0,-110010,0,100000).

FORMULA

From Colin Barker, Jan 11 2016: (Start)

a(n) = 10011*a(n-2)-110010*a(n-4)+100000*a(n-6) for n>10.

G.f.: (1 +110*x -9901*x^2 +8891*x^3 -880100*x^4 +8881000*x^5 -999110000*x^6 +10991100000*x^7 -999000000000*x^8 -11000000000*x^9 +1000000000000*x^10) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 -10*x^2)).

(End)

MATHEMATICA

rule=103; 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 -9901*x^2 +8891*x^3 -880100*x^4 +8881000*x^5 -999110000*x^6 +10991100000*x^7 -999000000000*x^8 -11000000000*x^9 +1000000000000*x^10) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 -10*x^2)) + O(x^20)) \\ Colin Barker, Jan 11 2016

CROSSREFS

Cf. A267136.

Sequence in context: A281173 A281219 A266979 * A039724 A008944 A106004

Adjacent sequences:  A267135 A267136 A267137 * A267139 A267140 A267141

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 10 2016

STATUS

approved

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Last modified December 19 02:36 EST 2018. Contains 318245 sequences. (Running on oeis4.)