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A266661 Decimal representation of the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell. 1
1, 6, 3, 124, 3, 2044, 3, 32764, 3, 524284, 3, 8388604, 3, 134217724, 3, 2147483644, 3, 34359738364, 3, 549755813884, 3, 8796093022204, 3, 140737488355324, 3, 2251799813685244, 3, 36028797018963964, 3, 576460752303423484, 3, 9223372036854775804, 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 03 2016 and Apr 18 2019: (Start)

a(n) = (7*(-1)^n+2^(2*n+1)-(-1)^n*2^(2*n+1)-1)/2 for n>1.

a(n) = 17*a(n-2)-16*a(n-4) for n>5.

G.f.: (1+6*x-14*x^2+22*x^3-32*x^4+32*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

a(n) = A266255(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 *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}] (* Decimal Representation of Rows *)

CROSSREFS

Cf. A266659.

Sequence in context: A002610 A100979 A279107 * A136133 A200020 A011487

Adjacent sequences:  A266658 A266659 A266660 * A266662 A266663 A266664

KEYWORD

nonn

AUTHOR

Robert Price, Jan 02 2016

STATUS

approved

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)