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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A267535 Binary representation of the n-th iteration of the "Rule 143" elementary cellular automaton starting with a single ON (black) cell. 1
1, 110, 11001, 1100111, 110011111, 11001111111, 1100111111111, 110011111111111, 11001111111111111, 1100111111111111111, 110011111111111111111, 11001111111111111111111, 1100111111111111111111111, 110011111111111111111111111, 11001111111111111111111111111 (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 (101,-100).

FORMULA

From Colin Barker, Jan 17 2016: (Start)

a(n) = 101*a(n-1)-100*a(n-2) for n>3.

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

(End)

MATHEMATICA

rule=143; 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

(PARI) Vec((1+10*x)*(1-x+x^2)/((1-x)*(1-100*x)) + O(x^20)) \\ Colin Barker, Jan 17 2016

CROSSREFS

Cf. A267533.

Sequence in context: A135645 A266299 A265696 * A267577 A262779 A058935

Adjacent sequences:  A267532 A267533 A267534 * A267536 A267537 A267538

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 16 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 26 18:36 EDT 2019. Contains 321511 sequences. (Running on oeis4.)