A267816 Decimal representation of the n-th iteration of the "Rule 221" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 23, 111, 479, 1983, 8063, 32511, 130559, 523263, 2095103, 8384511, 33546239, 134201343, 536838143, 2147418111, 8589803519, 34359476223, 137438429183, 549754765311, 2199021158399, 8796088827903, 35184363700223, 140737471578111, 562949919866879

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 22 2016 and Apr 16 2019: (Start)

a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3) for n>3.

G.f.: (1-4*x+16*x^2-16*x^3) / ((1-x)*(1-2*x)*(1-4*x)).

(End)

a(n) = 2^(n + 1) * (2^n - 1) - 1, for n > 0. - Jaroslav Krizek, Jan 22 2017

Mathematica

rule=221; 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 *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}]   (* Decimal Representation of Rows *)

Crossrefs

Cf. A267814.

Similar entries: A085601 (2^(n + 1) * (2^n + 1) + 1), A092431 (2^(n - 1) * (2^n + 1) - 1), A092440 (2^(n + 1) * (2^n - 1) + 1), A129868 (2^(n - 1) * (2^n - 1) - 1), A134169 (2^(n - 1) * (2^n - 1) + 1), A281481 (2^(n - 1) * (2^n + 1) + 1), A281482 (2^(n + 1) * (2^n + 1) - 1). - Jaroslav Krizek, Jan 22 2017

Sequence in context: A196970 A197557 A225671 * A269235 A245752 A290367

Adjacent sequences: A267813 A267814 A267815 * A267817 A267818 A267819

Keyword

nonn,easy

Author

Robert Price, Jan 20 2016

Status

approved