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A267614 Decimal representation of the n-th iteration of the "Rule 185" elementary cellular automaton starting with a single ON (black) cell. 1
1, 1, 11, 47, 191, 767, 3071, 12287, 49151, 196607, 786431, 3145727, 12582911, 50331647, 201326591, 805306367, 3221225471, 12884901887, 51539607551, 206158430207, 824633720831, 3298534883327, 13194139533311, 52776558133247, 211106232532991, 844424930131967 (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 18 2016 and Apr 20 2019: (Start)

a(n) = 5*a(n-1)-4*a(n-2) for n>3.

G.f.: (1-4*x+10*x^2-4*x^3) / ((1-x)*(1-4*x)).

(End)

Empirical a(n) = 3*4^(n-1)-1 for n>1. - Colin Barker, Nov 25 2016 and Apr 20 2019

MATHEMATICA

rule=185; 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. A198693, A267612.

Sequence in context: A076306 A219079 A059323 * A123984 A141282 A067355

Adjacent sequences:  A267611 A267612 A267613 * A267615 A267616 A267617

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 18 2016

STATUS

approved

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Last modified June 16 06:46 EDT 2019. Contains 324145 sequences. (Running on oeis4.)