A267045 Decimal representation of the middle column of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 4, 8, 17, 34, 69, 138, 277, 554, 1109, 2218, 4437, 8874, 17749, 35498, 70997, 141994, 283989, 567978, 1135957, 2271914, 4543829, 9087658, 18175317, 36350634, 72701269, 145402538, 290805077, 581610154, 1163220309, 2326440618, 4652881237, 9305762474

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 10 2016 and Apr 17 2019: (Start)

a(n) = (2*(-1)^n+13*2^n-6)/12 for n>1.

a(n) = 2*a(n-1)+a(n-2)-2*a(n-3) for n>4. [Typo corrected by Karl V. Keller, Jr., Mar 16 2022]

G.f.: (1-x^2+x^4) / ((1-x)*(1+x)*(1-2*x)).

(End)

Mathematica

rule=91; 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. A267015, A267044.

Sequence in context: A098718 A018299 A083593 * A266446 A018093 A214083

Adjacent sequences: A267042 A267043 A267044 * A267046 A267047 A267048

Keyword

nonn,easy

Author

Robert Price, Jan 09 2016

Status

approved