A266217 Binary representation of the n-th iteration of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.

1, 110, 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..499

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 25 2015 and Apr 13 2019: (Start)

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

G.f.: (1 + 110*x - 10001*x^2 + 11001*x^3 + 10000*x^4 - 10000*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 - 0^abs(n-1). - Karl V. Keller, Jr., Aug 26 2021

Mathematica

rule=7; 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 - 0**abs(n-1) for n in range(50)]) # Karl V. Keller, Jr., Aug 26 2021

Crossrefs

Cf. A266216, A266218.

Sequence in context: A352466 A096209 A287469 * A229084 A242568 A278865

Adjacent sequences: A266214 A266215 A266216 * A266218 A266219 A266220

Keyword

nonn,easy

Author

Robert Price, Dec 24 2015

Status

approved