A267055 Decimal representation of the n-th iteration of the "Rule 93" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 20, 47, 336, 703, 5440, 11007, 87296, 175103, 1397760, 2797567, 22368256, 44744703, 357908480, 715849727, 5726601216, 11453333503, 91625881600, 183252287487, 1466015154176, 2932032405503, 23456246661120, 46912501710847, 375299963355136, 750599960264703

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 10 2016 and Apr 19 2019: (Start)

a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>5.

G.f.: (1+3*x-x^2-16*x^3-32*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).

(End)

Mathematica

rule=93; 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. A267053, A267054.

Sequence in context: A268602 A344890 A072472 * A296252 A211068 A343010

Adjacent sequences: A267052 A267053 A267054 * A267056 A267057 A267058

Keyword

nonn,easy

Author

Robert Price, Jan 09 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