A266445 Binary representation of the middle column of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 100, 1000, 10001, 100010, 1000101, 10001010, 100010101, 1000101011, 10001010110, 100010101100, 1000101011000, 10001010110001, 100010101100010, 1000101011000101, 10001010110001010, 100010101100010101, 1000101011000101010, 10001010110001010101

Offset

0,2

References

Stephen 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

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Dec 31 2015 and Apr 16 2019: (Start)

a(n) = (-9*(-1)^n+9901000008901*2^(n-10)*5^(n-11)-11)/198 for n>10.

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

(End)

Conjecture: a(n) = floor(9901000008901*10^n/9900000000000). - Karl V. Keller, Jr., Jan 30 2022

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]], {k, 1, rows}]  (* Binary Representation of Middle Column *)

Crossrefs

Cf. A266441, A266444, A266446.

Sequence in context: A138824 A273495 A267044 * A266896 A282981 A282951

Adjacent sequences: A266442 A266443 A266444 * A266446 A266447 A266448

Keyword

nonn,easy

Author

Robert Price, Dec 29 2015

Status

approved