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A267354 Number of OFF (white) cells in the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell. 1
0, 1, 2, 1, 6, 1, 10, 1, 14, 1, 18, 1, 22, 1, 26, 1, 30, 1, 34, 1, 38, 1, 42, 1, 46, 1, 50, 1, 54, 1, 58, 1, 62, 1, 66, 1, 70, 1, 74, 1, 78, 1, 82, 1, 86, 1, 90, 1, 94, 1, 98, 1, 102, 1, 106, 1, 110, 1, 114, 1, 118, 1, 122, 1, 126, 1, 130, 1, 134, 1, 138, 1 (list; graph; refs; listen; history; text; internal format)
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 14 2016: (Start)

a(n) = ((2*(-1)^n+2)*n-3*(-1)^n-1)/2 for n>0.

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

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

(End)

a(n) = A266303(n-1). - R. J. Mathar, Jan 17 2016

MATHEMATICA

rule=123; 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. A267349.

Sequence in context: A302129 A191093 A266303 * A139625 A053785 A233809

Adjacent sequences:  A267351 A267352 A267353 * A267355 A267356 A267357

KEYWORD

nonn

AUTHOR

Robert Price, Jan 13 2016

STATUS

approved

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Last modified May 7 00:59 EDT 2021. Contains 343621 sequences. (Running on oeis4.)