A267805 Decimal representation of the n-th iteration of the "Rule 214" elementary cellular automaton starting with a single ON (black) cell.

1, 7, 23, 103, 375, 1639, 6007, 26215, 96119, 419431, 1537911, 6710887, 24606583, 107374183, 393705335, 1717986919, 6299285367, 27487790695, 100788565879, 439804651111, 1612617054071, 7036874417767, 25801872865143, 112589990684263, 412829965842295

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

A. J. Macfarlane, Generating functions for integer sequences defined by the evolution of cellular automata..., Fig. 14.

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 22 2016 and Apr 20 2019: (Start)

a(n) = 17*a(n-2)-16*a(n-4) for n>3.

G.f.: (1+7*x+6*x^2-16*x^3) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

Mathematica

rule=214; 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. A071040.

Sequence in context: A217233 A316734 A096327 * A154113 A340889 A053706

Adjacent sequences: A267802 A267803 A267804 * A267806 A267807 A267808

Keyword

nonn,easy

Author

Robert Price, Jan 20 2016

Status

approved