A266673 Binary representation of the n-th iteration of the "Rule 57" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 1010, 1001011, 1001100, 11001010111, 1001011000, 111001001101111, 1001010110000, 1111001001011011111, 1001001101100000, 11111001001010110111111, 1001001011011000000, 111111001001001101101111111, 1001001010110110000000, 1111111001001001011011011111111

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 -10001*x^2 +989000*x^3 -1000000*x^5 -899991000*x^6 +10000000*x^7 +10911000000*x^8 -20000000000*x^10) / ((1 -x)*(1 +x)*(1 -10*x)*(1 -100*x)*(1 +100*x)*(1 -10*x^2)*(1 +10*x +100*x^2)*(1 -1000*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]]], {k, 1, rows}] (* Binary Representation of Rows *)

Crossrefs

Cf. A266672.

Sequence in context: A076940 A173521 A266442 * A055473 A317526 A235775

Adjacent sequences: A266670 A266671 A266672 * A266674 A266675 A266676

Keyword

nonn

Author

Robert Price, Jan 02 2016

Status

approved