A267210 Decimal representation of the middle column of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 7, 14, 29, 59, 118, 237, 475, 950, 1901, 3803, 7606, 15213, 30427, 60854, 121709, 243419, 486838, 973677, 1947355, 3894710, 7789421, 15578843, 31157686, 62315373, 124630747, 249261494, 498522989, 997045979, 1994091958, 3988183917, 7976367835

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 13 2016 and Apr 19 2019: (Start)

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

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

(End)

Mathematica

rule=109; 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. A243566.

Sequence in context: A125899 A266791 A052997 * A074988 A265381 A066225

Adjacent sequences: A267207 A267208 A267209 * A267211 A267212 A267213

Keyword

nonn,easy,changed

Author

Robert Price, Jan 11 2016

Status

approved