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A267888 Decimal representation of the n-th iteration of the "Rule 237" elementary cellular automaton starting with a single ON (black) cell. 2
1, 2, 31, 127, 511, 2047, 8191, 32767, 131071, 524287, 2097151, 8388607, 33554431, 134217727, 536870911, 2147483647, 8589934591, 34359738367, 137438953471, 549755813887, 2199023255551, 8796093022207, 35184372088831, 140737488355327, 562949953421311 (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 17 2019: (Start)
a(n) = 5*a(n-1)-4*a(n-2) for n>3.
G.f.: (1-3*x+25*x^2-20*x^3) / ((1-x)*(1-4*x)).
(End)
a(n) = 2^(2*n+1) - 1 for n>1. - Colin Barker, Nov 25 2016
MATHEMATICA
rule=237; 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. A267870.
Sequence in context: A107170 A273403 A291052 * A229014 A042059 A343830
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 21 2016
STATUS
approved

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Last modified May 27 11:15 EDT 2024. Contains 372858 sequences. (Running on oeis4.)