A266668 Decimal representation of the n-th iteration of the "Rule 51" elementary cellular automaton starting with a single ON (black) cell.

1, 5, 4, 119, 16, 2015, 64, 32639, 256, 523775, 1024, 8386559, 4096, 134209535, 16384, 2147450879, 65536, 34359607295, 262144, 549755289599, 1048576, 8796090925055, 4194304, 140737479966719, 16777216, 2251799780130815, 67108864, 36028796884746239, 268435456

Offset

0,2

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

Conjectures from Colin Barker, Jan 03 2016 and Apr 18 2019: (Start)

a(n) = (-1/2-(-4)^n+(-2)^n+(-1)^n/2+4^n).

G.f.: (1+7*x-3*x^2+8*x^3+32*x^4) / ((1-x)*(1+x)*(1+2*x)*(1-4*x)*(1+4*x)).

(End)

Conjecture: a(n) = 2*4^n - 2^n - 1 for odd n; a(n) = 2^n for even n. - Karl V. Keller, Jr., Oct 12 2021

Mathematica

rule=51; 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. A266666, A266667.

Sequence in context: A264880 A128191 A186639 * A043299 A144776 A371264

Adjacent sequences: A266665 A266666 A266667 * A266669 A266670 A266671

Keyword

nonn

Author

Robert Price, Jan 02 2016

Status

approved