A267589 Decimal representation of the middle column of the "Rule 169" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 5, 10, 20, 41, 83, 167, 335, 671, 1343, 2687, 5375, 10751, 21503, 43007, 86015, 172031, 344063, 688127, 1376255, 2752511, 5505023, 11010047, 22020095, 44040191, 88080383, 176160767, 352321535, 704643071, 1409286143, 2818572287, 5637144575, 11274289151

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+x^2-x^3+x^5) / ((1-x)*(1-2*x)).

(End)

Mathematica

rule=169; 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. A264442.

Sequence in context: A266613 A266462 A293319 * A006836 A129847 A330456

Adjacent sequences: A267586 A267587 A267588 * A267590 A267591 A267592

Keyword

nonn,easy

Author

Robert Price, Jan 18 2016

Status

approved