A266244 Binary representation of the n-th iteration of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.

1, 0, 101, 1100000, 11101, 11110100000, 11101, 111111110100000, 11101, 1111111111110100000, 11101, 11111111111111110100000, 11101, 111111111111111111110100000, 11101, 1111111111111111111111110100000, 11101, 11111111111111111111111111110100000, 11101

Offset

0,3

References

S. 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

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

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

a(n) = 10001*a(n-2) - 10000*a(n-4) for n>7.

G.f.: (1 -9900*x^2 +1100000*x^3 -989000*x^4 +109000000*x^5 -110000000*x^6 +10000000000*x^7) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)).

(End)

a(n) = floor(100^n/10) + floor(1011010*100^n/999900) - 1011010 for odd n>3; a(n) = 11101 for even n>3. - Karl V. Keller, Jr., Aug 19 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 *) Table[FromDigits[catri[[k]]], {k, 1, rows}]   (* Binary Representation of Rows *)

Prog

(Python) print([1, 0, 101, 1100000]+[100**n//10 + 1011010*100**n//999900 - 1011010 if n%2 else 11101 for n in range(4, 30)]) # Karl V. Keller, Jr., Aug 19 2021

Crossrefs

Cf. A266243, A266245.

Sequence in context: A031982 A015041 A317957 * A138120 A266609 A082521

Adjacent sequences: A266241 A266242 A266243 * A266245 A266246 A266247

Keyword

nonn,easy

Author

Robert Price, Dec 25 2015

Status

approved