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

0,2

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 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)

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 *)

Crossrefs

Cf. A267050, A267051.

Sequence in context: A283706 A284402 A284543 * A267009 A116606 A188132

Adjacent sequences: A267049 A267050 A267051 * A267053 A267054 A267055

Keyword

nonn,easy

Author

Robert Price, Jan 09 2016

Status

approved