A267270 Binary representation of the n-th iteration of the "Rule 115" elementary cellular automaton starting with a single ON (black) cell.

1, 101, 1100, 1101111, 1100000, 11101111111, 1100000000, 111101111111111, 1100000000000, 1111101111111111111, 1100000000000000, 11111101111111111111111, 1100000000000000000, 111111101111111111111111111, 1100000000000000000000, 1111111101111111111111111111111

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

Index entries for linear recurrences with constant coefficients, signature (0,11001,0,-10011000,0,10000000).

Formula

Empirical g.f.: (1 + 101*x - 9901*x^2 - 9990*x^3 - 990100*x^4 - 1100000*x^5 + 1000000*x^6) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-1000*x^2)). - Colin Barker, Jan 14 2016 and Apr 19 2019

Conjecture: a(n) = (10^(2*n + 1) - 9*10^(3*n/2 - 1/2) - 1)/9 for odd n; a(n) = 1100*10^(3*n/2 - 3) for even n > 0. - Karl V. Keller, Jr., Apr 02 2022

Mathematica

rule=115; 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. A267269, A267271.

Sequence in context: A099182 A048177 A283504 * A280340 A283589 A284403

Adjacent sequences: A267267 A267268 A267269 * A267271 A267272 A267273

Keyword

nonn,easy

Author

Robert Price, Jan 12 2016

Status

approved