A267614 Decimal representation of the n-th iteration of the "Rule 185" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 11, 47, 191, 767, 3071, 12287, 49151, 196607, 786431, 3145727, 12582911, 50331647, 201326591, 805306367, 3221225471, 12884901887, 51539607551, 206158430207, 824633720831, 3298534883327, 13194139533311, 52776558133247, 211106232532991, 844424930131967

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 18 2016 and Apr 20 2019: (Start)

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

G.f.: (1-4*x+10*x^2-4*x^3) / ((1-x)*(1-4*x)).

(End)

Empirical a(n) = 3*4^(n-1)-1 for n>1. - Colin Barker, Nov 25 2016 and Apr 20 2019

Mathematica

rule=185; 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. A198693, A267612, A267613.

Sequence in context: A076306 A219079 A059323 * A123984 A141282 A336181

Adjacent sequences: A267611 A267612 A267613 * A267615 A267616 A267617

Keyword

nonn,easy

Author

Robert Price, Jan 18 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022

Status

approved