A266283 Binary representation of the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 101, 1101010, 10101, 11110101010, 1010101, 111111010101010, 101010101, 1111111101010101010, 10101010101, 11111111110101010101010, 1010101010101, 111111111111010101010101010, 101010101010101, 1111111111111101010101010101010, 10101010101010101

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..999

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 (0,10101,0,-1010100,0,1000000).

Formula

From Colin Barker, Dec 27 2015 and Apr 14 2019: (Start)

a(n) = 10101*a(n-2) - 1010100*a(n-4) + 1000000*a(n-6) for n>5.

G.f.: (1+10*x-10000*x^2+1000000*x^3-1100000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).

(End)

a(n) = (10*100^n - (1000*10^n-1)/11 - 1)/9 for odd n; a(n) = (100*10^n-1)/99 for even n. - Karl V. Keller, Jr., Aug 29 2021

Mathematica

rule=13; 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

(Python) print([(10*100**n - (1000*10**n-1)//11 - 1)//9 if n%2 else (100*10**n-1)//99 for n in range(50)]) # Karl V. Keller, Jr., Aug 29 2021

Crossrefs

Cf. A266282, A266284.

Sequence in context: A036299 A061107 A015498 * A309540 A039393 A199168

Adjacent sequences: A266280 A266281 A266282 * A266284 A266285 A266286

Keyword

nonn,easy

Author

Robert Price, Dec 26 2015

Status

approved