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A266379 Binary representation of the n-th iteration of the "Rule 21" elementary cellular automaton starting with a single ON (black) cell. 3
1, 11, 0, 1111111, 0, 11111111111, 0, 111111111111111, 0, 1111111111111111111, 0, 11111111111111111111111, 0, 111111111111111111111111111, 0, 1111111111111111111111111111111, 0, 11111111111111111111111111111111111, 0, 111111111111111111111111111111111111111 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Robert Price, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (0,10001,0,-10000).

FORMULA

From Colin Barker, Dec 29 2015: (Start)

a(n) = 10001*a(n-2) - 10000*a(n-4) for n>5.

G.f.: (1 + 11*x - 10001*x^2 + 1001100*x^3 + 10000*x^4 - 1000000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)). (End)

a(n) = (1-(-1)^n)*(1000*10000^floor(n/2)-1)/18 for n>1. - Bruno Berselli, Dec 29 2015

a(n) = (10*100^n - 1)/9*(n mod 2) + 0^n - 100*0^abs(n-1). - Karl V. Keller, Jr., Sep 03 2021

MATHEMATICA

rule=21; 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

(Magma) [n le 1 select 11^n else (1-(-1)^n)*(1000*10000^Floor(n/2)-1)/18: n in [0..40]]; // Bruno Berselli, Dec 29 2015

(Python) print([(10*100**n - 1)//9*(n%2) + 0**n - 100*0**abs(n-1) for n in range(50)]) # Karl V. Keller, Jr., Sep 03 2021

CROSSREFS

Cf. A266377, A266380.

Sequence in context: A036931 A165399 A157712 * A158215 A294254 A216792

Adjacent sequences:  A266376 A266377 A266378 * A266380 A266381 A266382

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 28 2015

STATUS

approved

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Last modified September 26 20:54 EDT 2022. Contains 357049 sequences. (Running on oeis4.)