A071033 a(n) = n-th state of cellular automaton generated by "Rule 94" when started with a single ON cell.

1, 111, 11011, 1110111, 110101011, 11101010111, 1101010101011, 111010101010111, 11010101010101011, 1110101010101010111, 110101010101010101011, 11101010101010101010111, 1101010101010101010101011, 111010101010101010101010111, 11010101010101010101010101011

Offset

0,2

Comments

a(n) has length 2n+1.

Links

Robert Price, Table of n, a(n) for n = 0..999

Eric Weisstein's World of Mathematics, Rule 94

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.

Index to Elementary Cellular Automata

Index entries for sequences related to cellular automata

Index entries for linear recurrences with constant coefficients, signature (0,10001,0,-10000).

Formula

Conjecture: a(n) = floor((1099*100^n + 9090)/990) + 1 for odd n > 1; a(n) = floor((1090*100^n + 10)/990) + 1 for even n > 1. - Karl V. Keller, Jr., Oct 25 2021

Mathematica

rule=94; 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]]], {k, 1, rows}]   (* Binary Representation of Rows *) (* Robert Price, Feb 21 2016 *)

Crossrefs

This sequence, A118101 and A118102 are equivalent descriptions of the Rule 94 automaton.

Sequence in context: A266809 A152764 A249183 * A267364 A265379 A265688

Adjacent sequences: A071030 A071031 A071032 * A071034 A071035 A071036

Keyword

nonn,easy

Author

Hans Havermann, May 26 2002

Extensions

Corrected by Hans Havermann, Jan 07 2012

Edited by N. J. A. Sloane, Oct 20 2015 at the suggestion of Michael De Vlieger and Kevin Ryde

More terms from Robert Price, Dec 06 2015

Status

approved