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A267352 Number of ON (black) cells in the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell. 1
1, 2, 3, 6, 3, 10, 3, 14, 3, 18, 3, 22, 3, 26, 3, 30, 3, 34, 3, 38, 3, 42, 3, 46, 3, 50, 3, 54, 3, 58, 3, 62, 3, 66, 3, 70, 3, 74, 3, 78, 3, 82, 3, 86, 3, 90, 3, 94, 3, 98, 3, 102, 3, 106, 3, 110, 3, 114, 3, 118, 3, 122, 3, 126, 3, 130, 3, 134, 3, 138, 3 (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 14 2016: (Start)

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

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

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

(End)

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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)

CROSSREFS

Cf. A267349.

Sequence in context: A129915 A019773 A109536 * A101401 A106834 A191658

Adjacent sequences:  A267349 A267350 A267351 * A267353 A267354 A267355

KEYWORD

nonn

AUTHOR

Robert Price, Jan 13 2016

STATUS

approved

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Last modified May 17 09:03 EDT 2021. Contains 343969 sequences. (Running on oeis4.)