A266791 Decimal representation of the middle column of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.

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

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

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, A266789, A266790.

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