A266179 Binary representation of the n-th iteration of the "Rule 6" elementary cellular automaton starting with a single ON (black) cell.

1, 110, 10000, 1100000, 100000000, 11000000000, 1000000000000, 110000000000000, 10000000000000000, 1100000000000000000, 100000000000000000000, 11000000000000000000000, 1000000000000000000000000, 110000000000000000000000000, 10000000000000000000000000000

Offset

0,2

Comments

Rules 38,134 and 166 also generate this sequence.

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

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

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

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

Formula

From Colin Barker, Dec 23 2015 and Apr 13 2019: (Start)

a(n) = 4^(n-1)*5^(2*n-1)*(21-(-1)^n).

a(n) = 10000*a(n-2) for n>1.

G.f.: (1+110*x) / ((1-100*x)*(1+100*x)). (End)

a(n) = 110*100^(n-1) for odd n; a(n) = 100^n for even n. - Karl V. Keller, Jr., Aug 11 2021

Mathematica

rule=6; 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([110*100**(n-1) if n%2 else 100**n for n in range(30)]) # Karl V. Keller, Jr., Aug 11 2021

Crossrefs

Cf. A266178, A266180.

Sequence in context: A111784 A146495 A063751 * A163664 A266844 A265319

Adjacent sequences: A266176 A266177 A266178 * A266180 A266181 A266182

Keyword

nonn,easy

Author

Robert Price, Dec 22 2015

Status

approved