A267877 Decimal representation of the n-th iteration of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.

1, 0, 21, 119, 511, 2047, 8191, 32767, 131071, 524287, 2097151, 8388607, 33554431, 134217727, 536870911, 2147483647, 8589934591, 34359738367, 137438953471, 549755813887, 2199023255551, 8796093022207, 35184372088831, 140737488355327, 562949953421311

Offset

0,3

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 20 2019: (Start)

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

G.f.: (1-5*x+25*x^2+14*x^3-32*x^5) / ((1-x)*(1-4*x)).

(End)

Empirical a(n) = 2^(2*n+1) - 1 for n>3. - Colin Barker, Nov 26 2016 and Apr 20 2019

Mathematica

rule=233; 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. A267868.

Sequence in context: A341570 A297316 A079417 * A183318 A204214 A074088

Adjacent sequences: A267874 A267875 A267876 * A267878 A267879 A267880

Keyword

nonn,easy

Author

Robert Price, Jan 21 2016

Status

approved