A267460 Number of OFF (white) cells in the n-th iteration of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 4, 6, 6, 8, 8, 10, 10, 12, 12, 14, 14, 16, 16, 18, 18, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40, 42, 42, 44, 44, 46, 46, 48, 48, 50, 50, 52, 52, 54, 54, 56, 56, 58, 58, 60, 60, 62, 62, 64, 64, 66, 66, 68

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 16 2016: (Start)

a(n) = (2*n-(-1)^n+5)/2 for n>1.

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

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

(End)

Mathematica

rule=133; 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. A267423.

Cf. A052928, A265283, A213222.

Sequence in context: A092517 A128558 A090346 * A092989 A065558 A235384

Adjacent sequences: A267457 A267458 A267459 * A267461 A267462 A267463

Keyword

nonn

Author

Robert Price, Jan 15 2016

Status

approved