login
A267596
Decimal representation of the n-th iteration of the "Rule 173" elementary cellular automaton starting with a single ON (black) cell.
2
1, 2, 15, 63, 255, 1023, 4095, 16383, 65535, 262143, 1048575, 4194303, 16777215, 67108863, 268435455, 1073741823, 4294967295, 17179869183, 68719476735, 274877906943, 1099511627775, 4398046511103, 17592186044415, 70368744177663, 281474976710655
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 18 2016 and Apr 20 2019: (Start)
a(n) = 5*a(n-1)-4*a(n-2) for n>3.
G.f.: (1-3*x+9*x^2-4*x^3) / ((1-x)*(1-4*x)).
(End)
Empirical a(n) = 4^n - 1 for n>1. - Colin Barker, Nov 25 2016 and Apr 20 2019
MATHEMATICA
rule=173; 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
Sequence in context: A000181 A047146 A084187 * A119904 A271828 A183264
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 18 2016
STATUS
approved