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A263245 Decimal representation of the n-th iteration of the "Rule 155" elementary cellular automaton starting with a single ON (black) cell. 1
1, 5, 19, 95, 319, 1535, 5119, 24575, 81919, 393215, 1310719, 6291455, 20971519, 100663295, 335544319, 1610612735, 5368709119, 25769803775, 85899345919, 412316860415, 1374389534719, 6597069766655, 21990232555519, 105553116266495, 351843720888319 (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 20 2016 and Apr 17 2019: (Start)

a(n) = a(n-1)+16*a(n-2)-16*a(n-3) for n>3.

G.f.: (1+4*x-2*x^2+12*x^3) / ((1-x)*(1-4*x)*(1+4*x)).

(End)

Empirical a(n) = (11*4^n-(-4)^n-8)/8 for n>0. - Colin Barker, Nov 25 2016 and Apr 17 2019

MATHEMATICA

rule=155; 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. A263243.

Sequence in context: A149807 A149808 A149809 * A346199 A020050 A106958

Adjacent sequences:  A263242 A263243 A263244 * A263246 A263247 A263248

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 17 2016

STATUS

approved

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Last modified September 17 19:02 EDT 2021. Contains 347489 sequences. (Running on oeis4.)