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A267530 Number of OFF (white) cells in the n-th iteration of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell. 2
0, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36 (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 17 2016 and Apr 20 2019: (Start)

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

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

(End)

MATHEMATICA

rule=141; 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. A267525.

Essentially the same as A008619.

Sequence in context: A047742 A302778 A203967 * A050292 A181627 A071521

Adjacent sequences:  A267527 A267528 A267529 * A267531 A267532 A267533

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 16 2016

STATUS

approved

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Last modified October 23 11:48 EDT 2019. Contains 328345 sequences. (Running on oeis4.)