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A266301 Binary representation of the n-th iteration of the "Rule 15" elementary cellular automaton starting with a single ON (black) cell. 1
1, 110, 1, 1111110, 1, 11111111110, 1, 111111111111110, 1, 1111111111111111110, 1, 11111111111111111111110, 1, 111111111111111111111111110, 1, 1111111111111111111111111111110, 1, 11111111111111111111111111111111110, 1, 111111111111111111111111111111111111110 (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..999

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

FORMULA

Conjectures from Colin Barker, Dec 28 2015 and Apr 15 2019: (Start)

a(n) = (19*(-1)^n+10^(2*n+1)-(-1)^n*10^(2*n+1)-1)/18.

a(n) = 10001*a(n-2) - 10000*a(n-4) for n>3.

G.f.: (1+110*x-10000*x^2+11000*x^3) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

MATHEMATICA

rule=15; 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 *)

CROSSREFS

Cf. A266300.

Sequence in context: A278956 A281629 A278754 * A163597 A266606 A308003

Adjacent sequences:  A266298 A266299 A266300 * A266302 A266303 A266304

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 26 2015

STATUS

approved

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Last modified August 15 12:50 EDT 2020. Contains 336501 sequences. (Running on oeis4.)