A267890 Decimal representation of the n-th iteration of the "Rule 239" elementary cellular automaton starting with a single ON (black) cell.

1, 6, 31, 127, 511, 2047, 8191, 32767, 131071, 524287, 2097151, 8388607, 33554431, 134217727, 536870911, 2147483647, 8589934591, 34359738367, 137438953471, 549755813887, 2199023255551, 8796093022207, 35184372088831, 140737488355327, 562949953421311

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 22 2016 and Apr 17 2019: (Start)

a(n) = 5*a(n-1)-4*a(n-2) for n>3.

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

(End)

Empirical a(n) = 2^(2*n+1) - 1 for n>1. - Colin Barker, Nov 25 2016

Mathematica

rule=239; 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. A267871.

Sequence in context: A003728 A216370 A225425 * A244199 A128568 A079924

Adjacent sequences: A267887 A267888 A267889 * A267891 A267892 A267893

Keyword

nonn,easy

Author

Robert Price, Jan 21 2016

Status

approved