A267003 Decimal representation of the n-th iteration of the "Rule 83" elementary cellular automaton starting with a single ON (black) cell.

1, 5, 8, 111, 64, 1919, 512, 31743, 4096, 516095, 32768, 8323071, 262144, 133693439, 2097152, 2143289343, 16777216, 34326183935, 134217728, 549487378431, 1073741824, 8793945538559, 8589934592, 140720308486143, 68719476736, 2251662374731775, 549755813888

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 08 2016 and Apr 19 2019: (Start)

a(n) = 25*a(n-2)-152*a(n-4)+128*a(n-6) for n>5.

G.f.: (1+2*x)*(1+3*x-23*x^2+32*x^3-48*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)).

(End)

Mathematica

rule=83; 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. A267001, A267002.

Sequence in context: A025518 A361225 A356826 * A151827 A258044 A162571

Adjacent sequences: A267000 A267001 A267002 * A267004 A267005 A267006

Keyword

nonn,easy

Author

Robert Price, Jan 08 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