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A266791 Decimal representation of the middle column of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell. 1
1, 3, 7, 14, 29, 58, 117, 234, 468, 937, 1875, 3751, 7502, 15005, 30010, 60021, 120042, 240085, 480170, 960341, 1920682, 3841365, 7682730, 15365461, 30730922, 61461845, 122923690, 245847381, 491694762, 983389525, 1966779050, 3933558101, 7867116202 (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

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 04 2016 and Apr 18 2019: (Start)

a(n) = (-(-1)^n+5627*2^(n-9)-3)/6 for n>9.

G.f.: (1+x-x^3-x^8+x^9+x^10-x^12) / ((1-x)*(1+x)*(1-2*x)).

(End)

MATHEMATICA

rule=61; 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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k], 2], {k, 1, rows}]  (* Binary Representation of Middle Column *)

CROSSREFS

Cf. A266786.

Sequence in context: A192065 A157672 A125899 * A052997 A267210 A074988

Adjacent sequences:  A266788 A266789 A266790 * A266792 A266793 A266794

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 03 2016

STATUS

approved

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Last modified July 6 07:26 EDT 2020. Contains 335476 sequences. (Running on oeis4.)