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A267805 Decimal representation of the n-th iteration of the "Rule 214" elementary cellular automaton starting with a single ON (black) cell. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 26 13:40 EDT 2021. Contains 346294 sequences. (Running on oeis4.)