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A267681 Decimal representation of the n-th iteration of the "Rule 201" elementary cellular automaton starting with a single ON (black) cell. 2
1, 0, 21, 99, 471, 1935, 8031, 32319, 130431, 522495, 2094591, 8381439, 33544191, 134189055, 536829951, 2147368959, 8589770751, 34359279615, 137438298111, 549753978879, 2199020634111, 8796085682175, 35184361603071, 140737458995199, 562949911478271 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The fact that only n cells to the left and right of the initially active cell are updated at step n (cf. A267679 for the binary representation) is contradictory to the usual treatment of a "Rule m" automaton, where all cells are updated depending on their neighborhood. See also the illustration of "Rule 201" on the MathWorld page. - M. F. Hasler, Jul 28 2018

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 19 2016: (Start)

a(n) = 5*a(n-1)-20*a(n-3)+16*a(n-4) for n>4.

G.f.: (1-5*x+21*x^2+14*x^3-40*x^4) / ((1-x)*(1-2*x)*(1+2*x)*(1-4*x)).

(End)

Conjecture: a(n) = 2*4^n - (n%2*2 + [n]*5)*2^(n-1) - 1, where [n] = 1 iff n > 0; n%2 = 1 iff n is odd. - M. F. Hasler, Jul 28 2018

MATHEMATICA

rule=201; 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. A267679.

Sequence in context: A178794 A140370 A124949 * A126408 A174080 A157329

Adjacent sequences:  A267678 A267679 A267680 * A267682 A267683 A267684

KEYWORD

nonn

AUTHOR

Robert Price, Jan 19 2016

STATUS

approved

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Last modified February 29 08:26 EST 2020. Contains 332355 sequences. (Running on oeis4.)