A266850 Decimal representation of the n-th iteration of the "Rule 71" elementary cellular automaton starting with a single ON (black) cell.

1, 6, 4, 123, 16, 2031, 64, 32703, 256, 524031, 1024, 8387583, 4096, 134213631, 16384, 2147467263, 65536, 34359672831, 262144, 549755551743, 1048576, 8796091973631, 4194304, 140737484161023, 16777216, 2251799796908031, 67108864, 36028796951855103, 268435456

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 05 2016 and Apr 18 2019: (Start)

a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>5.

G.f.: (1+6*x-17*x^2-3*x^3+16*x^4-48*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).

(End)

Mathematica

rule=71; 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. A266848, A266849.

Sequence in context: A308900 A354949 A239861 * A109873 A334806 A014403

Adjacent sequences: A266847 A266848 A266849 * A266851 A266852 A266853

Keyword

nonn,easy

Author

Robert Price, Jan 04 2016

Status

approved