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A266283 Binary representation of the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell. 1
1, 10, 101, 1101010, 10101, 11110101010, 1010101, 111111010101010, 101010101, 1111111101010101010, 10101010101, 11111111110101010101010, 1010101010101, 111111111111010101010101010, 101010101010101, 1111111111111101010101010101010, 10101010101010101 (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 27 2015 and Apr 14 2019: (Start)

a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>5.

G.f.: (1+10*x-10000*x^2+1000000*x^3-1100000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).

(End)

MATHEMATICA

rule=13; 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. A266282.

Sequence in context: A036299 A061107 A015498 * A309540 A039393 A199168

Adjacent sequences:  A266280 A266281 A266282 * A266284 A266285 A266286

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 26 2015

EXTENSIONS

Conjectures from Colin Barker, Apr 14 2019

STATUS

approved

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Last modified February 25 10:28 EST 2020. Contains 332224 sequences. (Running on oeis4.)