A266301 Binary representation of the n-th iteration of the "Rule 15" elementary cellular automaton starting with a single ON (black) cell.

1, 110, 1, 1111110, 1, 11111111110, 1, 111111111111110, 1, 1111111111111111110, 1, 11111111111111111111110, 1, 111111111111111111111111110, 1, 1111111111111111111111111111110, 1, 11111111111111111111111111111111110, 1, 111111111111111111111111111111111111110

Offset

0,2

Links

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

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) = (19*(-1)^n+10^(2*n+1)-(-1)^n*10^(2*n+1)-1)/18.

a(n) = 10001*a(n-2) - 10000*a(n-4) for n>3.

G.f.: (1+110*x-10000*x^2+11000*x^3) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

a(n) = (10*100^n - 10)/9 for odd n; a(n) = 1 for even n. - Karl V. Keller, Jr., Aug 31 2021

E.g.f.: cosh(x) + 10*(sinh(100*x) - sinh(x))/9. - Stefano Spezia, Sep 02 2021

Mathematica

rule=15; 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 - 10)//9 if n%2 else 1 for n in range(50)]) # Karl V. Keller, Jr., Aug 31 2021

Crossrefs

Cf. A266300, A266302.

Sequence in context: A278956 A281629 A278754 * A163597 A266606 A308003

Adjacent sequences: A266298 A266299 A266300 * A266302 A266303 A266304

Keyword

nonn,easy

Author

Robert Price, Dec 26 2015

Status

approved