A267886 Decimal representation of the n-th iteration of the "Rule 235" elementary cellular automaton starting with a single ON (black) cell.

1, 4, 27, 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 20 2019: (Start)

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

G.f.: (1-x+11*x^2+8*x^3-16*x^4) / ((1-x)*(1-4*x)).

(End)

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

Mathematica

rule=235; 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. A267869.

Sequence in context: A267685 A190584 A268598 * A034512 A366486 A240194

Adjacent sequences: A267883 A267884 A267885 * A267887 A267888 A267889

Keyword

nonn,easy

Author

Robert Price, Jan 21 2016

Status

approved