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

Author

Robert Price, Jan 18 2016

Keywords

• nonn
• easy

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

Crossrefs

Cf. A086224, A265186, A266678, A266680.

Programs

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 *)

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)