A266460 Binary representation of the n-th iteration of the "Rule 27" elementary cellular automaton starting with a single ON (black) cell.

1, 101, 10, 1111011, 100, 11111110111, 1000, 111111111101111, 10000, 1111111111111011111, 100000, 11111111111111110111111, 1000000, 111111111111111111101111111, 10000000, 1111111111111111111111011111111, 100000000, 11111111111111111111111110111111111

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, Dec 31 2015 and Apr 16 2019: (Start)

a(n) = 10011*a(n-2)-110010*a(n-4)+100000*a(n-6) for n>5.

G.f.: (1+101*x-10001*x^2+99900*x^3+10000*x^4-110000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-10*x^2)).

(End)

Conjecture: a(n) = (10*(100^n - 9*10^floor(n/2)) - 1)/9 for odd n; a(n) = 10^(n/2) for even n. - Karl V. Keller, Jr., Sep 29 2021

Mathematica

rule=27; 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. A266459, A266461.

Sequence in context: A281840 A282222 A282199 * A341634 A060386 A062584

Adjacent sequences: A266457 A266458 A266459 * A266461 A266462 A266463

Keyword

nonn,easy

Author

Robert Price, Dec 29 2015

Status

approved