A266446 Decimal representation of the middle column of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 4, 8, 17, 34, 69, 138, 277, 555, 1110, 2220, 4440, 8881, 17762, 35525, 71050, 142101, 284202, 568405, 1136810, 2273621, 4547242, 9094485, 18188970, 36377941, 72755882, 145511765, 291023530, 582047061, 1164094122, 2328188245, 4656376490, 9312752981

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, Dec 30 2015 and Apr 16 2019: (Start)

a(n) = (-(-1)^n+6661*2^(n-10)-3)/6 for n>10.

G.f.: (1-x^2+x^4+x^9-x^10-x^11+x^13) / ((1-x)*(1+x)*(1-2*x)).

(End)

Conjecture: a(n) = floor(6661*2^n/6144). - Karl V. Keller, Jr., Dec 26 2021

Mathematica

rule=25; 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. A266441, A266444, A266445.

Sequence in context: A018299 A083593 A267045 * A018093 A214083 A026743

Adjacent sequences: A266443 A266444 A266445 * A266447 A266448 A266449

Keyword

nonn,easy

Author

Robert Price, Dec 29 2015

Status

approved