login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A267688 Binary representation of the n-th iteration of the "Rule 199" elementary cellular automaton starting with a single ON (black) cell. 1
1, 110, 11100, 1111010, 111110100, 11111101010, 1111111010100, 111111110101010, 11111111101010100, 1111111111010101010, 111111111110101010100, 11111111111101010101010, 1111111111111010101010100, 111111111111110101010101010, 11111111111111101010101010100 (list; graph; refs; listen; history; text; internal format)
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

Index entries for linear recurrences with constant coefficients, signature (110,-999,-110,1000).

FORMULA

From Colin Barker, Jan 19 2016: (Start)

a(n) = 110*a(n-1)-999*a(n-2)-110*a(n-3)+1000*a(n-4) for n>4.

G.f.: (1-x^2+10*x^3-1000*x^4) / ((1-x)*(1+x)*(1-10*x)*(1-100*x)).

(End)

MATHEMATICA

rule=199; 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 *)

Join[{1}, LinearRecurrence[{110, -999, -110, 1000}, {110, 11100, 1111010, 111110100}, 20]] (* Vincenzo Librandi, Jan 19 2016 *)

PROG

(PARI) Vec((1-x^2+10*x^3-1000*x^4)/((1-x)*(1+x)*(1-10*x)*(1-100*x)) + O(x^20)) \\ Colin Barker, Jan 19 2016

CROSSREFS

Cf. A267687.

Sequence in context: A265320 A109241 A090490 * A211979 A135650 A193240

Adjacent sequences:  A267685 A267686 A267687 * A267689 A267690 A267691

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 19 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 19:07 EST 2018. Contains 317214 sequences. (Running on oeis4.)