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A266664 Number of OFF (white) cells in the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell. 1
0, 1, 3, 2, 7, 2, 11, 2, 15, 2, 19, 2, 23, 2, 27, 2, 31, 2, 35, 2, 39, 2, 43, 2, 47, 2, 51, 2, 55, 2, 59, 2, 63, 2, 67, 2, 71, 2, 75, 2, 79, 2, 83, 2, 87, 2, 91, 2, 95, 2, 99, 2, 103, 2, 107, 2, 111, 2, 115, 2, 119, 2, 123, 2, 127, 2, 131, 2, 135, 2, 139, 2 (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 03 2016 and Apr 18 2019: (Start)

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

a(n) = 2*a(n-2)-a(n-4) for n>5.

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

(End)

a(n) = A266258(n), n>1. - R. J. Mathar, Jan 10 2016

MATHEMATICA

rule=47; 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. A266659.

Sequence in context: A200593 A249112 A265219 * A245601 A296513 A099378

Adjacent sequences:  A266661 A266662 A266663 * A266665 A266666 A266667

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 02 2016

STATUS

approved

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Last modified May 19 04:06 EDT 2019. Contains 323377 sequences. (Running on oeis4.)