A266721 Decimal representation of the middle column of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 5, 11, 22, 45, 90, 181, 362, 725, 1450, 2901, 5802, 11605, 23210, 46421, 92842, 185685, 371370, 742741, 1485482, 2970965, 5941930, 11883861, 23767722, 47535445, 95070890, 190141781, 380283562, 760567125, 1521134250, 3042268501, 6084537002, 12169074005

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Formula

From Colin Barker, Jan 05 2016 and Apr 17 2019: (Start)

a(n) = (-2*(-1)^n+17*2^n-6)/12 for n>1.

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

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

a(n) = floor(17*2^n/12). - Karl V. Keller, Jr., Oct 17 2021

Mathematica

rule=59; 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 *)

Prog

(Python) print([17*2**n//12  for n in range(50)]) # Karl V. Keller, Jr., Oct 18 2021

Crossrefs

Cf. A266716, A266719, A266720.

Sequence in context: A293362 A362583 A084188 * A044432 A033120 A365243

Adjacent sequences: A266718 A266719 A266720 * A266722 A266723 A266724

Keyword

nonn,easy

Author

Robert Price, Jan 03 2016

Status

approved