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

Stephen 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.

Stephen 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 (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

E.g.f.: exp(-x)*(-165 - 202*exp(2*x) + 3700*exp(101*x))/3333. - Elmo R. Oliveira, Feb 28 2026

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