A266323 Binary representation of the n-th iteration of the "Rule 19" elementary cellular automaton starting with a single ON (black) cell.

1, 101, 0, 1111111, 0, 11111111111, 0, 111111111111111, 0, 1111111111111111111, 0, 11111111111111111111111, 0, 111111111111111111111111111, 0, 1111111111111111111111111111111, 0, 11111111111111111111111111111111111, 0, 111111111111111111111111111111111111111

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..500

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

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

Formula

From Colin Barker, Dec 28 2015 and Apr 15 2019: (Start)

a(n) = 10001*a(n-2) - 10000*a(n-4) for n>5.

G.f.: (1+101*x-10001*x^2+101010*x^3+10000*x^4-100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

a(n) = (10*100^n - 1)/9*(n mod 2) + 0^n - 10*0^abs(n-1). - Karl V. Keller, Jr., Sep 02 2021

Mathematica

rule=19; 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 *)

Prog

(Python) print([(10*100**n - 1)//9*(n%2) + 0**n - 10*0**abs(n-1) for n in range(50)]) # Karl V. Keller, Jr., Sep 02 2021

Crossrefs

Cf. A266155, A266324.

Sequence in context: A279699 A279602 A168588 * A280372 A181721 A277917

Adjacent sequences: A266320 A266321 A266322 * A266324 A266325 A266326

Keyword

nonn,easy

Author

Robert Price, Dec 27 2015

Status

approved