login
A267816
Decimal representation of the n-th iteration of the "Rule 221" elementary cellular automaton starting with a single ON (black) cell.
3
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.
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
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 20 2016
STATUS
approved