A267351 Decimal representation of the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell.

1, 5, 14, 119, 56, 2015, 224, 32639, 896, 523775, 3584, 8386559, 14336, 134209535, 57344, 2147450879, 229376, 34359607295, 917504, 549755289599, 3670016, 8796090925055, 14680064, 140737479966719, 58720256, 2251799780130815, 234881024, 36028796884746239

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 14 2016 and Apr 19 2019: (Start)

a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>6.

G.f.: (1+5*x-7*x^2+14*x^3-154*x^4-64*x^5+160*x^6) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).

(End)

Mathematica

rule=123; 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. A267349, A267350.

Sequence in context: A316233 A317154 A283785 * A058072 A027304 A070135

Adjacent sequences: A267348 A267349 A267350 * A267352 A267353 A267354

Keyword

nonn,easy

Author

Robert Price, Jan 13 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022

Status

approved