A260692 Binary representation of the n-th iteration of the "Rule 17" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 1000, 1001111, 1000000, 11001111111, 1000000000, 111001111111111, 1000000000000, 1111001111111111111, 1000000000000000, 11111001111111111111111, 1000000000000000000, 111111001111111111111111111, 1000000000000000000000, 1111111001111111111111111111111

Offset

0,3

Comments

Rule 49 also generates this sequence.

Links

Robert Price, Table of n, a(n) for n = 0..1000

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 (0,11001,0,-10011000,0,10000000).

Formula

From Colin Barker, Dec 29 2015 and Apr 15 2019: (Start)

a(n) = 11001*a(n-2)-10011000*a(n-4)+10000000*a(n-6) for n>5.

G.f.: (1+x-10001*x^2+990110*x^3+10000*x^4-2100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-1000*x^2)). - Colin Barker, Dec 29 2015

(End)

a(n) = (10*100^n - 990*1000^((n-1)/2) - 1)/9 for odd n; a(n) = 1000^(n/2) for even n. - Karl V. Keller, Jr., Aug 31 2021

Mathematica

rule=17; 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 - 990*1000**((n-1)//2) - 1)//9 if n%2 else 1000**(n//2) for n in range(50)]) # Karl V. Keller, Jr., Aug 31 2021

Crossrefs

Cf. A260552, A266090.

Sequence in context: A029802 A060365 A060366 * A234605 A013793 A013856

Adjacent sequences: A260689 A260690 A260691 * A260693 A260694 A260695

Keyword

nonn,easy

Author

Robert Price, Dec 27 2015

Status

approved