

A266327


Binary representation of the nth iteration of the "Rule 20" elementary cellular automaton starting with a single ON (black) cell.


1



1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11
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OFFSET

0,2


COMMENTS

Rules 52, 148 and 180 also generate this sequence.


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


FORMULA

Conjectures from Colin Barker, Dec 28 2015 and Apr 18 2019: (Start)
a(n) = 65*(1)^n.
a(n) = a(n2) for n>1.
G.f.: (1+11*x) / ((1x)*(1+x)).
(End)


MATHEMATICA

rule=20; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rowsk+1, rows+k1}], {k, 1, rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]]], {k, 1, rows}] (* Binary Representation of Rows *)


CROSSREFS

Cf. A266326.
Sequence in context: A231920 A230891 A063431 * A274216 A280524 A317845
Adjacent sequences: A266324 A266325 A266326 * A266328 A266329 A266330


KEYWORD

nonn,easy


AUTHOR

Robert Price, Dec 27 2015


STATUS

approved



