A267596 Decimal representation of the n-th iteration of the "Rule 173" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 15, 63, 255, 1023, 4095, 16383, 65535, 262143, 1048575, 4194303, 16777215, 67108863, 268435455, 1073741823, 4294967295, 17179869183, 68719476735, 274877906943, 1099511627775, 4398046511103, 17592186044415, 70368744177663, 281474976710655

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

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.: (1-3*x+9*x^2-4*x^3) / ((1-x)*(1-4*x)).

(End)

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

Mathematica

rule=173; 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. A267594, A267595.

Sequence in context: A000181 A047146 A084187 * A119904 A271828 A183264

Adjacent sequences: A267593 A267594 A267595 * A267597 A267598 A267599

Keyword

nonn,easy

Author

Robert Price, Jan 18 2016

Status

approved