The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A266720 Binary representation of the middle column of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell. 3
1, 10, 101, 1011, 10110, 101101, 1011010, 10110101, 101101010, 1011010101, 10110101010, 101101010101, 1011010101010, 10110101010101, 101101010101010, 1011010101010101, 10110101010101010, 101101010101010101, 1011010101010101010, 10110101010101010101 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
From Colin Barker, Jan 04 2016 and Apr 18 2019: (Start)
a(n) = (-450*(-1)^n+10009*10^n-550)/9900 for n>1.
a(n) = 10*a(n-1)+a(n-2)-10*a(n-3) for n>4.
G.f.: (1+x^3-x^4) / ((1-x)*(1+x)*(1-10*x)).
(End)
a(n) = floor(10009*10^n/9900). - Karl V. Keller, Jr., Oct 17 2021
MATHEMATICA
rule=59; 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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k]], {k, 1, rows}] (* Binary Representation of Middle Column *)
PROG
(Python) print([10009*10**n//9900 for n in range(50)]) # Karl V. Keller, Jr., Oct 18 2021
CROSSREFS
Sequence in context: A284137 A284179 A096883 * A033128 A094945 A190480
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 03 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 27 23:16 EDT 2024. Contains 372900 sequences. (Running on oeis4.)