A266674 Decimal representation of the n-th iteration of the "Rule 57" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 10, 75, 76, 1623, 600, 29295, 4784, 496351, 37728, 8164799, 300736, 132422527, 2403712, 2133112575, 19192576, 34244750847, 153466368, 548835613695, 1227582464, 8788730820607, 9818265600, 140678589542399, 78541336576, 2251328604004351, 628321116160

Offset

0,3

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

Empirical g.f.: (1 +x -17*x^2 +40*x^3 -64*x^5 -248*x^6 +128*x^7 +1472*x^8 -2048*x^10) / ((1 -x)*(1 +x)*(1 -2*x)*(1 -4*x)*(1 +4*x)*(1 -2*x^2)*(1 +2*x +4*x^2)*(1 -8*x^2)). - Colin Barker, Jan 03 2016 and Apr 18 2019

Mathematica

rule=57; 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. A266672.

Sequence in context: A103434 A119167 A233100 * A233455 A027778 A026969

Adjacent sequences: A266671 A266672 A266673 * A266675 A266676 A266677

Keyword

nonn

Author

Robert Price, Jan 02 2016

Status

approved