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A266439 Number of OFF (white) cells in the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell. 1
0, 0, 5, 0, 9, 0, 13, 0, 17, 0, 21, 0, 25, 0, 29, 0, 33, 0, 37, 0, 41, 0, 45, 0, 49, 0, 53, 0, 57, 0, 61, 0, 65, 0, 69, 0, 73, 0, 77, 0, 81, 0, 85, 0, 89, 0, 93, 0, 97, 0, 101, 0, 105, 0, 109, 0, 113, 0, 117, 0, 121, 0, 125, 0, 129, 0, 133, 0, 137, 0, 141, 0 (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..500

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, Dec 30 2015 and Apr 15 2019: (Start)

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

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

G.f.: x^2*(5-x^2) / ((1-x)^2*(1+x)^2).

(End)

a(n) = A266222(n), n>1. - R. J. Mathar, Jan 10 2016

MATHEMATICA

rule=23; 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. A266434.

Sequence in context: A141431 A166011 A266222 * A132706 A199184 A159692

Adjacent sequences:  A266436 A266437 A266438 * A266440 A266441 A266442

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 29 2015

STATUS

approved

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Last modified July 4 15:25 EDT 2020. Contains 335448 sequences. (Running on oeis4.)