

A266841


Binary representation of the nth iteration of the "Rule 69" elementary cellular automaton starting with a single ON (black) cell.


1



1, 10, 10100, 101011, 101010000, 1010101111, 1010101000000, 10101010111111, 10101010100000000, 101010101011111111, 101010101010000000000, 1010101010101111111111, 1010101010101000000000000, 10101010101010111111111111, 10101010101010100000000000000
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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


FORMULA

Conjectures from Colin Barker, Jan 05 2016 and Apr 18 2019: (Start)
a(n) = 10101*a(n2)1010100*a(n4)+1000000*a(n6) for n>5.
G.f.: (1+10*xx^2+x^3110000*x^5) / ((1x)*(1+x)*(110*x)*(1+10*x)*(1100*x)*(1+100*x)).
(End)


MATHEMATICA

rule=69; 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. A266840.
Sequence in context: A317959 A119037 A327232 * A267677 A101305 A001098
Adjacent sequences: A266838 A266839 A266840 * A266842 A266843 A266844


KEYWORD

nonn,easy


AUTHOR

Robert Price, Jan 04 2016


STATUS

approved



