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A267780 Decimal representation of the n-th iteration of the "Rule 211" elementary cellular automaton starting with a single ON (black) cell. 2
1, 5, 25, 125, 505, 2045, 8185, 32765, 131065, 524285, 2097145, 8388605, 33554425, 134217725, 536870905, 2147483645, 8589934585, 34359738365, 137438953465, 549755813885, 2199023255545, 8796093022205, 35184372088825, 140737488355325, 562949953421305 (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
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
Conjectures from Colin Barker, Jan 20 2016 and Apr 20 2019: (Start)
a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3) for n>3.
G.f.: (1+x+4*x^2+24*x^3) / ((1-x)*(1+x)*(1-4*x)).
(End)
MATHEMATICA
rule=211; 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
Sequence in context: A015950 A337950 A366323 * A228736 A126642 A269615
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 20 2016
EXTENSIONS
Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - N. J. A. Sloane, Jun 13 2022
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)