A267526 Binary representation of the n-th iteration of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 101, 1011, 1010111, 10101111, 10101011111, 101010111111, 101010101111111, 1010101011111111, 1010101010111111111, 10101010101111111111, 10101010101011111111111, 101010101010111111111111, 101010101010101111111111111, 1010101010101011111111111111

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 16 2016: (Start)

a(n) = 11*a(n-1) + 9990*a(n-2) - 110000*a(n-3) + 100000*a(n-4) for n > 5.

G.f.: (1 - x - 9999*x^2 + 10000*x^3 + 990000*x^4 - 1000000*x^5) / ((1-x)*(1-10*x)*(1-100*x)*(1+100*x)). - [corrected by Karl V. Keller, Jr., Sep 18 2021]

(End)

Conjecture: a(n) = 10^n*(100^floor(n/2) - 1)/99 + (10^(n-1) - 1)/9 for n > 1. - Karl V. Keller, Jr., Sep 22 2021

Mathematica

rule=141; 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. A267525, A267527.

Sequence in context: A261200 A175541 A180175 * A261199 A041041 A333344

Adjacent sequences: A267523 A267524 A267525 * A267527 A267528 A267529

Keyword

nonn

Author

Robert Price, Jan 16 2016

Status

approved