A266724 Number of OFF (white) cells in the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.

0, 1, 3, 1, 7, 1, 11, 1, 15, 1, 19, 1, 23, 1, 27, 1, 31, 1, 35, 1, 39, 1, 43, 1, 47, 1, 51, 1, 55, 1, 59, 1, 63, 1, 67, 1, 71, 1, 75, 1, 79, 1, 83, 1, 87, 1, 91, 1, 95, 1, 99, 1, 103, 1, 107, 1, 111, 1, 115, 1, 119, 1, 123, 1, 127, 1, 131, 1, 135, 1, 139, 1

Offset

0,3

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

Paul Barry, On a Central Transform of Integer Sequences, arXiv:2004.04577 [math.CO], 2020.

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 05 2016 and Apr 18 2019: (Start)

a(n) = (-1)^n*(n-1)+n for n>0.

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

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

(End)

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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White cells in stage n *)

Crossrefs

Cf. A266716.

Sequence in context: A086665 A273013 A050521 * A247146 A362628 A225561

Adjacent sequences: A266721 A266722 A266723 * A266725 A266726 A266727

Keyword

nonn

Author

Robert Price, Jan 03 2016

Status

approved