A267604 Decimal representation of the middle column of the "Rule 175" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 6, 13, 27, 55, 111, 223, 447, 895, 1791, 3583, 7167, 14335, 28671, 57343, 114687, 229375, 458751, 917503, 1835007, 3670015, 7340031, 14680063, 29360127, 58720255, 117440511, 234881023, 469762047, 939524095, 1879048191, 3758096383, 7516192767

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 18 2016 and Apr 20 2019: (Start)

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

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

Conjectures from Altug Alkan, Jan 18 2016: (Start)

a(n) = A086224(n-2), for n > 1.

a(n) = ceiling((7/4)*2^n - 1). (End)

Mathematica

rule=175; 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], 2], {k, 1, rows}]  (* Binary Representation of Middle Column *)

Crossrefs

Cf. A086224, A265186, A266678, A266680.

Sequence in context: A092539 A094386 A371902 * A099036 A391680 A131246

Adjacent sequences: A267601 A267602 A267603 * A267605 A267606 A267607

Keyword

nonn,easy

Author

Robert Price, Jan 18 2016

Status

approved