

A267681


Decimal representation of the nth 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
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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(n1)20*a(n3)+16*a(n4) for n>4.
G.f.: (15*x+21*x^2+14*x^340*x^4) / ((1x)*(12*x)*(1+2*x)*(14*x)).
(End)
Conjecture: a(n) = 2*4^n  (n%2*2 + [n]*5)*2^(n1)  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}, rows1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rowsk+1, rows+k1}], {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



