A266661 Decimal representation of the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.

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

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

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

Conjecture: a(n) = 2*4^n - 4 for odd n > 1; a(n) = 3 for even n > 1. - Karl V. Keller, Jr., Oct 10 2021

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. A266255, A266659, A266660.

Sequence in context: A002610 A100979 A279107 * A136133 A200020 A375254

Adjacent sequences: A266658 A266659 A266660 * A266662 A266663 A266664

Keyword

nonn,easy

Author

Robert Price, Jan 02 2016

Status

approved