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A267847 Decimal representation of the n-th iteration of the "Rule 227" elementary cellular automaton starting with a single ON (black) cell. 1
1, 4, 26, 122, 506, 2042, 8186, 32762, 131066, 524282, 2097146, 8388602, 33554426, 134217722, 536870906, 2147483642, 8589934586, 34359738362, 137438953466, 549755813882, 2199023255546, 8796093022202, 35184372088826, 140737488355322, 562949953421306 (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 21 2016: (Start)

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

G.f.: (1-x+10*x^2+8*x^3) / ((1-x)*(1-4*x)).

(End)

Conjecture: a(n) = 2*(4^n - 3) for n>1. - Colin Barker, Nov 26 2016

MATHEMATICA

rule=227; 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. A267845.

Sequence in context: A140804 A147621 A246854 * A211166 A245460 A261738

Adjacent sequences:  A267844 A267845 A267846 * A267848 A267849 A267850

KEYWORD

nonn

AUTHOR

Robert Price, Jan 21 2016

STATUS

approved

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Last modified May 20 12:33 EDT 2019. Contains 323422 sequences. (Running on oeis4.)