A263245 Decimal representation of the n-th iteration of the "Rule 155" elementary cellular automaton starting with a single ON (black) cell.

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

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

Conjecture: a(n) = 3*4^((n-1)/2)*2^n - 1 for odd n; a(n) = 5*4^(n/2 - 1)*2^n - 1 for even n > 0. - Karl V. Keller, Jr., May 01 2022

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, A263244.

Sequence in context: A149808 A371836 A149809 * A346199 A020050 A106958

Adjacent sequences: A263242 A263243 A263244 * A263246 A263247 A263248

Keyword

nonn,easy

Author

Robert Price, Jan 17 2016

Status

approved