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A267921 Decimal representation of the n-th iteration of the "Rule 243" elementary cellular automaton starting with a single ON (black) cell. 5
1, 5, 29, 125, 509, 2045, 8189, 32765, 131069, 524285, 2097149, 8388605, 33554429, 134217725, 536870909, 2147483645, 8589934589, 34359738365, 137438953469, 549755813885, 2199023255549, 8796093022205, 35184372088829, 140737488355325, 562949953421309 (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
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
Conjectures from Colin Barker, Jan 22 2016 and Apr 16 2019: (Start)
a(n) = 5*a(n-1)-4*a(n-2) for n>2.
G.f.: (1+8*x^2) / ((1-x)*(1-4*x)).
(End)
Empirical a(n) = 2^(2*n+1) - 3 for n>0. - Colin Barker, Nov 25 2016
MATHEMATICA
rule=243; 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. A267919.
Sequence in context: A153077 A000352 A327133 * A241676 A291889 A217325
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 22 2016
STATUS
approved

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Last modified May 26 16:22 EDT 2024. Contains 372840 sequences. (Running on oeis4.)