A266247 Binary representation of the middle column of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 101, 1010, 10101, 101011, 1010110, 10101101, 101011010, 1010110101, 10101101010, 101011010101, 1010110101010, 10101101010101, 101011010101010, 1010110101010101, 10101101010101010, 101011010101010101, 1010110101010101010, 10101101010101010101

Offset

0,2

References

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

Links

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

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (10,1,-10).

Formula

From Colin Barker, Dec 28 2015 and Apr 14 2019: (Start)

a(n) = (-45000*(-1)^n + 1000009*10^n - 55000)/990000 for n > 3.

a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3) for n > 6.

G.f.: (1 + x^5 - x^6) / ((1-x)*(1+x)*(1-10*x)).

(End)

a(n) = floor((100000*10^n/9 + 100001*10^n)/110000). - Karl V. Keller, Jr., Dec 15 2021

Mathematica

rule=9; 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([(100000*10**n//9 + 100001*10**n)//110000 for n in range(50)]) # Karl V. Keller, Jr., Dec 15 2021

Crossrefs

Cf. A266243, A266248.

Sequence in context: A056830 A280146 A279665 * A267443 A267879 A284137

Adjacent sequences: A266244 A266245 A266246 * A266248 A266249 A266250

Keyword

nonn,easy

Author

Robert Price, Dec 25 2015

Status

approved