A262863 Binary representation of the middle column of the "Rule 147" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 100, 1001, 10011, 100110, 1001100, 10011001, 100110011, 1001100110, 10011001100, 100110011001, 1001100110011, 10011001100110, 100110011001100, 1001100110011001, 10011001100110011, 100110011001100110, 1001100110011001100, 10011001100110011001

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

Formula

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

a(n) = 11*a(n-1)-11*a(n-2)+11*a(n-3)-10*a(n-4) for n>3.

G.f.: (1-x+x^2) / ((1-x)*(1-10*x)*(1+x^2)).

(End)

a(n) = floor(100100*10^n/99990). - Karl V. Keller, Jr., Aug 21 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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k]], {k, 1, rows}]  (* Binary Representation of Middle Column *)

Prog

(Python) print([100100*10**n//99990 for n in range(50)]) # Karl V. Keller, Jr., Aug 21 2021

Crossrefs

Cf. A262808, A262864.

Sequence in context: A102397 A132347 A215254 * A267156 A267524 A259883

Adjacent sequences: A262860 A262861 A262862 * A262864 A262865 A262866

Keyword

nonn,easy

Author

Robert Price, Jan 17 2016

Status

approved