A266671 Decimal representation of the n-th iteration of the "Rule 53" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 8, 95, 64, 1791, 512, 30719, 4096, 507903, 32768, 8257535, 262144, 133169151, 2097152, 2139095039, 16777216, 34292629503, 134217728, 549218942975, 1073741824, 8791798054911, 8589934592, 140703128616959, 68719476736, 2251524935778303, 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

S. 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 03 2016 and Apr 18 2019: (Start)

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

G.f.: (1+3*x-17*x^2+20*x^3+16*x^4-128*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)).

(End)

Mathematica

rule=53; 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. A266669, A266670.

Sequence in context: A070901 A079657 A136309 * A069703 A114737 A233163

Adjacent sequences: A266668 A266669 A266670 * A266672 A266673 A266674

Keyword

nonn

Author

Robert Price, Jan 02 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - N. J. A. Sloane, Jun 13 2022

Status

approved