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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 5 03:48 EST 2023. Contains 360082 sequences. (Running on oeis4.)