A267052 Decimal representation of the n-th iteration of the "Rule 92" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 7, 11, 23, 43, 87, 171, 343, 683, 1367, 2731, 5463, 10923, 21847, 43691, 87383, 174763, 349527, 699051, 1398103, 2796203, 5592407, 11184811, 22369623, 44739243, 89478487, 178956971, 357913943, 715827883, 1431655767, 2863311531, 5726623063, 11453246123

Offset: 0

Author

Robert Price, Jan 09 2016

Keywords

• nonn
• easy

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

Crossrefs

Cf. A267050, A267051.

Programs

Mathematica

rule=92; 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 *)

Formula

Conjectures from Colin Barker, Jan 10 2016 and Apr 17 2019: (Start)

a(n) = (3+2*(-1)^n+2^(2+n))/3 for n>0.

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

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

(End)