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A266842 Decimal representation of the n-th iteration of the "Rule 69" elementary cellular automaton starting with a single ON (black) cell. 1
1, 2, 20, 43, 336, 687, 5440, 10943, 87296, 174847, 1397760, 2796543, 22368256, 44740607, 357908480, 715833343, 5726601216, 11453267967, 91625881600, 183252025343, 1466015154176, 2932031356927, 23456246661120, 46912497516543, 375299963355136, 750599943487487 (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

FORMULA

Conjectures from Colin Barker, Jan 05 2016 and Apr 18 2019: (Start)

a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>5.

G.f.: (1+2*x-x^2+x^3-48*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).

(End)

MATHEMATICA

rule=69; 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]], 2], {k, 1, rows}]   (* Decimal Representation of Rows *)

CROSSREFS

Cf. A266840.

Sequence in context: A293930 A194999 A280436 * A254542 A202602 A097652

Adjacent sequences:  A266839 A266840 A266841 * A266843 A266844 A266845

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 04 2016

STATUS

approved

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Last modified December 12 22:06 EST 2019. Contains 329963 sequences. (Running on oeis4.)