A262861 Binary representation of the n-th iteration of the "Rule 147" elementary cellular automaton starting with a single ON (black) cell.

1, 101, 10001, 1011101, 100010001, 10111011101, 1000100010001, 101110111011101, 10001000100010001, 1011101110111011101, 100010001000100010001, 10111011101110111011101, 1000100010001000100010001, 101110111011101110111011101, 10001000100010001000100010001

Offset

0,2

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 (0,10001,0,-10000).

Formula

From Colin Barker, Jan 17 2016 and Apr 17 2019: (Start)

a(n) = 10001*a(n-2) - 10000*a(n-4) for n>3.

G.f.: (1+101*x+1000*x^3) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

a(n) = floor((10000 + 110*(n mod 2))*100^n/9999). - Karl V. Keller, Jr., Aug 11 2021

Mathematica

rule=147; 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([(10000 + 110*(n%2))*100**n//9999 for n in range(30)]) # Karl V. Keller, Jr., Aug 11 2021

Crossrefs

Cf. A262862, A262808.

Sequence in context: A152756 A265172 A153500 * A371563 A164367 A263244

Adjacent sequences: A262858 A262859 A262860 * A262862 A262863 A262864

Keyword

nonn,easy

Author

Robert Price, Jan 17 2016

Status

approved