A266788 Decimal representation of the n-th iteration of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 12, 87, 120, 1679, 976, 29823, 7808, 500735, 62464, 8200191, 499712, 132710399, 3997696, 2135425023, 31981568, 34263269375, 255852544, 548984061951, 2046820352, 8789919006719, 16374562816, 140688096231423, 130996502528, 2251404676694015, 1047972020224

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 03 2016 and Apr 18 2019: (Start)

a(n) = 25*a(n-2)-152*a(n-4)+128*a(n-6) for n>10.

G.f.: (1+3*x-13*x^2+12*x^3-28*x^4-40*x^5-328*x^6+688*x^7+112*x^8 -768*x^9+256*x^10) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)).

(End)

Mathematica

rule=61; 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. A266786, A266787.

Sequence in context: A077047 A074505 A260912 * A039305 A174463 A367143

Adjacent sequences: A266785 A266786 A266787 * A266789 A266790 A266791

Keyword

nonn,easy

Author

Robert Price, Jan 03 2016

Status

approved