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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A267596 Decimal representation of the n-th iteration of the "Rule 173" elementary cellular automaton starting with a single ON (black) cell. 1
1, 2, 15, 63, 255, 1023, 4095, 16383, 65535, 262143, 1048575, 4194303, 16777215, 67108863, 268435455, 1073741823, 4294967295, 17179869183, 68719476735, 274877906943, 1099511627775, 4398046511103, 17592186044415, 70368744177663, 281474976710655 (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 (5,-4).

FORMULA

From Colin Barker, Jan 18 2016: (Start)

a(n) = 5*a(n-1)-4*a(n-2) for n>3.

G.f.: (1-3*x+9*x^2-4*x^3) / ((1-x)*(1-4*x)).

(End)

a(n) = 4^n - 1 for n>1. - Colin Barker, Nov 25 2016

MATHEMATICA

rule=173; 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]], 2], {k, 1, rows}]   (* Decimal Representation of Rows *)

PROG

(PARI) Vec((1-3*x+9*x^2-4*x^3)/((1-x)*(1-4*x)) + O(x^30)) \\ Colin Barker, Jan 18 2016

CROSSREFS

Cf. A267594.

Sequence in context: A000181 A047146 A084187 * A119904 A271828 A117669

Adjacent sequences:  A267593 A267594 A267595 * A267597 A267598 A267599

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 18 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 October 20 11:06 EDT 2018. Contains 316379 sequences. (Running on oeis4.)