A267156 Binary representation of the middle column of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 100, 1001, 10011, 100111, 1001111, 10011111, 100111111, 1001111111, 10011111110, 100111111101, 1001111111010, 10011111110101, 100111111101010, 1001111111010101, 10011111110101010, 100111111101010101, 1001111111010101010, 10011111110101010101

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

Conjectures from Colin Barker, Jan 11 2016 and Apr 19 2019: (Start)

a(n) = (-9*(-1)^n+9910999999*2^(n-7)*5^(n-8)-11)/198 for n>7.

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

G.f.: (1-x^2+x^3+x^4-x^10) / ((1-x)*(1+x)*(1-10*x)).

(End)

Mathematica

rule=107; 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 *)

Crossrefs

Cf. A267152.

Sequence in context: A132347 A215254 A262863 * A267524 A259883 A242808

Adjacent sequences: A267153 A267154 A267155 * A267157 A267158 A267159

Keyword

nonn,easy

Author

Robert Price, Jan 11 2016

Status

approved