A265688 Binary representation of the n-th iteration of the "Rule 190" elementary cellular automaton starting with a single ON (black) cell.

1, 111, 11101, 1110111, 111011101, 11101110111, 1110111011101, 111011101110111, 11101110111011101, 1110111011101110111, 111011101110111011101, 11101110111011101110111, 1110111011101110111011101, 111011101110111011101110111, 11101110111011101110111011101

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..499

Eric Weisstein's World of Mathematics, Rule 190

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (100,1,-100).

Formula

From Colin Barker, Dec 13 2015 and Apr 18 2019: (Start)

a(n) = (-165*(-1)^n+37*100^(n+1)-202)/3333.

a(n) = (37*100^(n+1)-367)/3333 for n even.

a(n) = (37*100^(n+1)-37)/3333 for n odd.

a(n) = 100*a(n-1) + a(n-2) - 100*a(n-3) for n>2.

G.f.: (1+11*x) / ((1-x)*(1+x)*(1-100*x)).

(End)

a(n) = floor(11100*100^n/9999). - Karl V. Keller, Jr., Aug 10 2021

Mathematica

rule = 190; rows = 20; Table[FromDigits[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]]], {k, 1, rows}]

Prog

(Python) print([11100*100**n//9999 for n in range(30)]) # Karl V. Keller, Jr., Aug 10 2021

Crossrefs

Cf. A037576 (decimal), A118111.

Sequence in context: A071033 A267364 A265379 * A138146 A100706 A259102

Adjacent sequences: A265685 A265686 A265687 * A265689 A265690 A265691

Keyword

nonn,easy

Author

Robert Price, Dec 13 2015

Status

approved