A263805 Binary representation of the n-th iteration of the "Rule 157" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 111, 101111, 1011111, 1010111111, 10101111111, 10101011111111, 101010111111111, 101010101111111111, 1010101011111111111, 1010101010111111111111, 10101010101111111111111, 10101010101011111111111111, 101010101010111111111111111

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 20 2016 and Apr 17 2019: (Start)

a(n) = 11*a(n-1)+9990*a(n-2)-110000*a(n-3)+100000*a(n-4) for n>4.

G.f.: (1-10000*x^2+100000*x^3-100000*x^4) / ((1-x)*(1-10*x)*(1-100*x)*(1+100*x)).

(End)

Conjecture: a(n) = (10*10^n*(10^n + 1)/11 - 1)/9 for odd n; a(n) = (10^n*(10^n + 10)/11 - 1)/9 for even n > 0. - Karl V. Keller, Jr., May 05 2022

Mathematica

rule=157; 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 *)

Crossrefs

Cf. A263804, A263806.

Sequence in context: A108047 A144784 A030175 * A058949 A378022 A119742

Adjacent sequences: A263802 A263803 A263804 * A263806 A263807 A263808

Keyword

nonn,easy

Author

Robert Price, Jan 17 2016

Status

approved