A266664 Number of OFF (white) cells in the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.

0, 1, 3, 2, 7, 2, 11, 2, 15, 2, 19, 2, 23, 2, 27, 2, 31, 2, 35, 2, 39, 2, 43, 2, 47, 2, 51, 2, 55, 2, 59, 2, 63, 2, 67, 2, 71, 2, 75, 2, 79, 2, 83, 2, 87, 2, 91, 2, 95, 2, 99, 2, 103, 2, 107, 2, 111, 2, 115, 2, 119, 2, 123, 2, 127, 2, 131, 2, 135, 2, 139, 2

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

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 03 2016 and Apr 18 2019: (Start)

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

a(n) = 2*a(n-2)-a(n-4) for n>5.

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

(End)

a(n) = A266258(n), n>1. - R. J. Mathar, Jan 10 2016

Mathematica

rule=47; 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. A266659.

Sequence in context: A249112 A265219 A349211 * A308439 A245601 A355934

Adjacent sequences: A266661 A266662 A266663 * A266665 A266666 A266667

Keyword

nonn,easy

Author

Robert Price, Jan 02 2016

Status

approved